UCEED 17 NAT SOLUTIONS

Q 1 . A 12 cm x 12 cm x 12 cm wooden cube is painted and its four views are shown below. this cube is  sliced into 64 smaller equal sized cubes of 3 cm x 3 cm x 3 cm. How many of these small cubes will have exactly one green face and exactly one orange face in the same cube ?

 Ans.

From fig we can say that the cube has 3 orange and three green surfaces and if it is  sliced into 64 smaller equal sized cubes of 3 cm x 3 cm x 3 cm.Then we have

1) corner 1to 8 cubes will have three colours.

2) center abcd and like wise will have single colour.

3) hatched cubes will have one orange and one green face.( other 3 faces ,hidden, are green )

    so we get 12 as ans.

Q 2 The following fig.is cloned and the cloned fig.is reflected along the xy axis .how many rectangles are present in the resultant fig.?

Ans 

1)first count rectangles in original fig as shown in A . there are eight rectangles.

2) after cloning and reflection similar eight rectangles are there.(total 16).

3) considering fig. together as in B  there are nine rectangles.(see colour wise to understand)

4)total 16+9 =25 rectangles.

Q 3 Shown below are pieces of a regular  polygon how many sides the polygon have?

Ans 3

Just count the vertex and the ans will be 7 .

Q4  How many different types of characters appear in the figure given below?

Ans 4 

28 different types of characters are there in the figure.

Q5 How many fonts are used in the given sets of words?

Ans 5

there are 11 fonts as shown.

observe the common letters,curves ,lines, angle at end of lines .

Bold and normal letters can be of same font.

Q 6 A shopkeeper is offering discounts for the festive season.The discount is based on a series.The following table depicts the first five combination of this series.The purchase amount and discount are in rupees.How much is the discount for a purchase of rupees 75,000?

Ans If we observe the chart we find that 

Difference between discount of first two combination is 30.

Difference between discount of second and third is 60. 

Difference between discount of third and fourth is 120.

Difference between discount of fourth and fifth is 240. 

i.e. in next combination discount is getting doubled . (purchase amount also getting doubled)

our next combination in series will be

           purchase                                    Discount

>_4801 and < 9601                              949   (difference of 480 from 5 term)

>_ 9601 and <19201                           1909  ( difference of 960 from 6 term)

>_ 19201 and < 38401                        3829 (difference of 1920 from 7 term)

>_ 38401 and <76801                         7669  (difference of 3840 from 8 term)

7669 is the  ans.

Q 7  Given the following equation, how many parrots are equal to one elephant?

Ans.

given that 

 1 parrot + 2 fish  = 4 elephants  ....................(1)

 2 parrots + 1 elephant = 1 fish + 1 parrot ...................(2)

solution

 from eq (2) we can say that 1 parrot + 1 elephant = 1 fish 

substituting in eq. (1) 

1 parrot + 2( 1 parrot + 1 elephant) = 4 elephants

1 parrot + 2 parrot + 2 elephants = 4 elephants

3 parrots = 2 elephants

3/2 parrots = 1 elephant 

ans is 1.5

Q 8 how many of the alphabets using the font shown below when flipped on the horizontal axis,can still be read as capital alphabets in the same font? 

Ans.

Alphabets when flipped on the horizontal axis and still can be read as capital alphabets in the same font are 

B C D E H I K M O W X ( M canbe read as W and W as M) ans is 11

Q 9  shown below in figure 1 is a layout of a chess board with one knight and several pawns. Given that the knight cannot land on any square that has pawn,but can jump over it ,the pawns cannot move,and the knight moves on a chess board as shown in fig.2, what is the least number of steps required for the knight to reach square x ?

ans 

Knight takes 8 steps to reach square X

Q 10 Shown below is a fan with red coloured patterns on it .when it rotates , the patterns make circles.How many red circles will be seen when the fan rotates?

ans 

There will be 8 red circles as shown in fig.  (some lines coincides) zigzag lines will not make circle.

Q11  Fig 1 has been constructed by overlapping some alphabets .Assuming the alphabets may be rotated, how many alphabets from fig 2 cannot be overlapped to fit within fig.1? 

Ans    first find out the overlapped alphabets they are B ,C (ROTATED) ,D,E,F,G (ROTATED)H,L,P,

 total 9 , 

so remaining 17 alphabets cannot be overlapped to fit within fig 1.

 (alphabets J,K,R may create confusion but their curve,inclined lines are different.)

Q12 Two gearsA and B with red arrows are shown below. Gear A rotates in clockwise direction.How many complete rotations does the gear B have to make for the red arrows to meet?

Ans  

   For red arrows of Gear A and Gear B to meet, 

   Arrow of  A should be at 4 and  B to be at B1  (see fig above)

    When Gear B rotates full 1 time Gear A position will be 7, like wise

                                            2 times Gear A position will be 3

                                             3 times Gear A position will be 10

                                             4 times Gear A position will be 6

                                             5 times Gear A position will be 2 

                                             6 times  Gear A position will be 9

                                             7 times Gear A position will be  5

                                              8 times Gear A position will be 1 

                                              9 times  Gear A position will be 8

                                             10 times Gear A position will be 4 ( required)

Gear B will make 10 complete rotation .  

(It can be solved by gear ratio method  )                              

Q13  Fig. 1 is an image composed of partial circles.Some cuts in the circle form the corners of triangles as shown in fig 2 What is the total number of triangles whose three corners are formed by three circles?

Ans 

  10 triangles are formed as shown by red .

 Q 14  There are two discs, one with numbers and other with three cut outs as shown in fig 1 and are overlapped as shown in fig 2.For every second,the numbered disc rotates two numbers in anticlockwise direction and the cut out disc rotates one number in the clockwise direction.If the arrangement at zero second is as shown in fig 2, what will be the number inside the pentagonal cut out at 5 seconds?

Ans   If the  numbered disc rotates two number in anticlockwise direction the the position of numbered disc will remain same.

        If the cut out disc rotates one number in the clockwise direction the pentagonal cut out will be at           3.

          so ans is 3.

Q 15  Fig. 1 is formed by a black square inscribed in a white circle which in turn is inscribed in another black square of side 2 cm as shown. If a point is chosen at random inside fig.1, what is the probability that the point will be in the area shaded black?

Ans. first find the area of black region

 area of outer square = 2 x 2 =4 sq cm

 area of circle = pie r x r = 3.14 x 1 ( diameter is 2 cm )

area of corner black region will be =outer square- circle = 4 - 3.14 = 0.86 sq.cm

In inner square Diagonal is 2 cm ( diameter of circle )

From Pythagoras theorem we can find sides

2 x 2 = (side x side) + (side x side)

2 x 2 = 2 (side x side )

side = 1.41

so area of black inner square = 1.41 x 1.41 = 1.98

Total black region = 0.86 + 1.98 = 2.84

 probability that the point will be in the area shaded black=  area of black region / total area

p = 2.84 / 4 = 0.71 Ans

Q 16  

Q 17  Shown below are two views of the same 3D object . How many non contiguous surfaces are there in the object ?

Ans 

 There are 36 surfaces as shown in fig. ( second top is one surface)

Q 18

Q 19  A 3 x 3 grid as shown in fig 1 is to be filled with numbers 1 to 9 according to the following rules : 

- 8 is above 9 and to the right of 2

- 3 is to the right of 7 and above 9 which is to the left of 4 

- 2 is to the left of 5

-7 is above 6 and 2

-1 is above 5  

'To the left of ' or 'to the right of' means in the same row 

Above or below means in the same column

What is the sum of the three numbers in the middle row?

Ans  From above rules we find the grid as shown

and the sum of the three numbers in the middle row = 15

UCEED 18 MSQ SOLUTIONS AND TIPS

 UCEED 18 MSQ  (SECTION B ) SOLUTIONS

UCEED 18  paper is divided into three sections, A, B and C.

Section A (80 Marks) contains a total of 20 Numerical Answer Type (NAT) questions.

Section B (100 Marks) contains a total of 25 Multiple Select Questions (MSQ).

Section C (120 Marks) contains a total of 40 Multiple Choice Questions (MCQ).

IN THIS POST UCEED 18 MSQ  (SECTION B ) SOLUTIONS ARE GIVEN

Q.21 On the left is a photograph. Which option(s) is/are part(s) of that photograph?

ANS On observing we see that B,C,D images are parts of that photograph.

Q.22 If spaces and special characters are ignored in the following text, which country/countries

is/are hidden in the text shown below?

I think the earth’s ecosystem will collapse very soon. Natural resources have been exploited for far

too long at the cost of the wellbeing of humankind, I am afraid. I don’t want to stir another controversy

but I ardently feel that the time has come for us to take urgent actions to save our planet from

manmade disasters.

A. Ghana

B. India

C. Peru

D. Iran

ANS As highlighted India and Iran (i.e, B and D ) are hidden in the text.


Tip : see the first letter of the option in the text for example G of Ghana ,it comes in long,well being, urgent then see the following next letters if that matches with the word Ghana.here the ans is no. Like wise check other options.

Q.23 The CBI is investigating a dangerous gang of three criminals. The criminals are Donga, Tirudan

and Daaku. The investigation team consists of Pradyuman, Daya, Fredricks, Salunkhe, Tarika and Purvi.

Each criminal is to be investigated by exactly two investigators, and each investigator investigates

exactly one criminal. The investigation is to be conducted subject to the following constraints:

Pradyuman and Daya do not investigate the same criminal.

Fredricks and Salunkhe investigate the same criminal.

If Fredricks investigates Tirudan, then Tarika must investigate Daaku.

Given these constrains, which of the following could be the acceptable assignment(s) of investigators

to potential criminals?

A. Fredricks & Salunkhe investigate Tirudan, Pradyuman & Daya investigate Donga and Tarika &

Purvi investigate Daaku

B. Fredricks & Salunkhe investigate Donga, Tarika & Pradyuman investigate Tirudan and Daya &

Purvi investigate Daaku

C. Tarika & Purvi investigate Donga, Fredricks & Pradyuman investigate Tirudan and Salunkhe &

Daya investigate Daaku

D. Daya & Purvi investigate Tirudan, Tarika & Pradyuman investigate Daaku and Fredricks &

Salunkhe investigate Donga.

ANS # As per the first constraint
Pradyuman and Daya do not investigate the same criminal. Option A is incorrect.
# Option B satisfies all constraints ,so it is correct.
#As per the constraint If Fredricks investigates Tirudan, then Tarika must investigate Daaku.
Option C is incorrect. / wrong
# Option D satisfies all constraints , so it is correct.

Q.24 If, 9 + 8 means 9 is the child of 8, and 7 * 6 means that 6 is the wife of 7, then which of the

following statements can be derived from 2 + 3 * 1 + 4 * 5?

A. 2 is the grandchild of 4

B. 1 is the daughter of 5

C. 5 is the grandfather of 3

D. 1 is the mother of 2

ANS Decoding 2 + 3 * 1 + 4 * 5 we can say that
2 is the child of 3 from (2+3)
1 is the wife of 3 from (3*1)
1 is the child of 4 from (1+4)
5 is the wife of 4 from ( 4*5)

Make hierarchy chart from the above information .
5 and 4 are grand parents
1 and 3 are parents
2 is child.

so options A,B,D are correct.
Tip : keep in mind the gender also in solving such problems.
to practice logical reasoning you can visit

          

https://www.indiabix.com/

Q.25 30 circles are given below, with a set of rules:

1. The bigger the circle, the farther away it is from us.

2. The thinner the line of the circle, the closer it is to us.

3. The red circles are farther away from us as compared to the blue circles.

Which of the options given below is/are TRUE?

         

A) Circle 25 is the closest to us

B) Circle 25 is farthest from us

C) Circle 24 is closer to us than circle 14

D) Circle 6 is closer to us than circle 8

ANS From above set of rules we conclude that smaller, thinner and blue circles are closer to us.

# circle 25 is smallest ,thinnest and blue ,so Option A is correct.
# circle 25 is closest therefore can not be farthest, Option B is incorrect.
# circle 24 and 14 are red and 24 is smaller ,so Option C is correct.
# circle 6 is thicker and bigger in size than 8 so it is farther ,Option D is incorrect.

Option A and C are correct ans.

Q.26 Which concept does this image by Escher illustrate?

A. Tessellation

B. Figure and Ground 

C. Mise en Scene

D. Collage

Let's see the terminology of above four concepts

# A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

# Figure–ground organization is a type of perceptual grouping which is a vital necessity for recognizing objects through vision. In Gestalt psychology it is known as identifying a figure from the background.

# The arrangement of everything that appears in the framing – actors, lighting, décor, props, costume – is called mise-en-scène, a French term that means “placing on stage.” The frame and camerawork are also considered part of the mise-en-scène of a movie.

# Collage is a piece of art made by sticking various different materials such as photographs and pieces of paper or fabric on to a backing.

ANS : from the above definitions option A and B  are correct.

Q.27 Read the passage given below, written by Nick Hughes:

“We tend to treat power as though it is intrinsically valuable. We seek it out and covet it, quite

irrespective of how we might wield it and what it might get us. One need only look at the history of

totalitarian politics to recognise this tendency in its most grotesque form. But power isn’t intrinsically

valuable, it’s only instrumentally valuable – valuable as a means to an end. And whether or not they

are objectively valuable, the ends that matter to us, the things that we care about most – our

relationships, our projects and goals, our shared experiences, social justice, the pursuit of knowledge,

the creation and appreciation of art, music and literature, and the future and fate of ours and other

species – do not depend to any considerable extent on our having control over a vast but largely

irrelevant Universe. We might be distinctly lacking in power from the cosmic perspective, and so, in a

sense, insignificant. But having such power and such significance wouldn’t make much of a difference

anyway. To lament its lack and respond with despair and nihilism is merely a form of narcissism. Most

of what matters to us is right here on Earth.”

Which of the statements is/are TRUE of the paragraph above:

A. The author argues that intrinsic value is distinct from instrumental value and that power

possesses the latter of the two.

B. “Humans and our significance in the universe”, is one of the themes discussed in the

passage.

C. The philosophies of nihilism and narcissism are suggested as remedies by the author.

D. The author suggests that we look at the history of totalitarian politics to recognise that we

shun power in the most grotesque form.

ANS A and B are correct options .

Q.28 Which option(s) is/are simple rotations of the figure given below?

ANS : option D is correct because internal hexagons colours are not same after rotation .

Q.29 Read the statements below:

All female and male natives in their country are strong.

Some men in their country are migrants.

All migrants in their country are not strong.

Not all migrants are women.

Based on the above, which conclusion(s) stated in the options is/are valid?

A. Some women in their country are strong.

B. Some migrants in their country are men.

C. Some people in their country are not strong.

D. All strong people in their country are women

ANS : A is correct ( native female are strong but migrants female are not strong).
           B is correct (because not all migrants are women).
           C is correct ( because migrants are not strong)
           D is wrong ( because all female and male natives in their country are strong.

Q.30 Which of the following words are similar in meaning?

A. Scribble

B. Doodle

C. Nibble

D. Feeble

  

meanings of of above words are 

# Scribble means write or draw (something) carelessly or hurriedly.
# Doodle means scribble absent-mindedly.
# Nibble means take small bites out of. or show cautious interest in a commercial opportunity
# Feeble means lacking physical strength, especially as a result of age or illness.

Ans : A and B are correct options.
  Q.31 Which of the following words is/are similar in meaning to ‘Centre’?
A. Heart
B. Core
C. Nucleus
D. Nub

ANS A,B,C,D

Q.32 Consider this poem:
Now, marriages happen in halls
They used to happen at home
Honeymoon too
Before they wandered into halls
Stage. Actors. Audiences from afar.
Receptions never really took place
Yet they would go on for days.
Now, receptions include
Those who don’t really figure.
Show face, shove envelope (gifts not accepted)
Grin for the camera.
Get out. Not all that bad.
Quick and efficient. No one really cares.
Which mood(s) does the poem evoke?
A. Cynicism
B. Nostalgia
C. Happiness
D. Lust

ANS : A,B

# Cynicism - Cynicism is an attitude or state of mind characterized by a general distrust of others' motives.
# Nostalgia -Nostalgia is a sentimentality for the past, typically for a period or place with happy personal associations.
# Happiness - positive or pleasant emotions ranging from contentment to intense joy.
# Lust - Lust is a craving, it can take any form such as the , lust for money or the lust for power.
 Q.33 Goethe said, “Doubt grows with knowledge”. From this perspective, who would a
knowledgeable person be?
A. One for whom doubt does not grow with knowledge
B. One who has no doubt
C. One who has doubt
D. One whose doubt grows with knowledge

ANS : C,D 

Q.34 Theory is already existing knowledge and Practice is knowledge that comes by ‘doing’.
Based on this statement which of the following is/are TRUE?
A. Theory precedes Practice.
B. Practice is knowledge in action.
C. Knowledge without ‘doing’ is Theory.
D. Theory and Practice are one and the same.

 ANS : A,B,C 

Q.35 Which of the following quotes celebrate(s) technology?
A. “Did that search engine really know what you want, or are you playing along, lowering your
standards to make it seem clever?”
B. “ I fear that we are beginning to design ourselves to suit digital models of us, and I worry
about a leaching (leakage) of empathy and humanity in the process”
C. “The approach to digital culture I abhor would indeed turn all the world’s book into one
book”.
D. “What a computer is to me is the most remarkable tool that we can ever come up with. It’s
the equivalent of a bicycle for our minds”.

ANS : D 

 Q.36 Consider the drip irrigation system in villages on hilly terrain. Which of the following
statements is/are correct?
A. Bamboo pipes can be used to divert perennial springs on the hilltops to the lower reaches by
gravity.
B. If the bamboo pipes have to cross a road they can be taken above the land.
C. This irrigation system is useful for the places with high ground water level.
D. The bamboo pipes could be replaced with PVC pipes.

ANS :A,B,D

Q.37 Six pacmen have joined hands to take revenge from an evil ghost. They are standing around
in a circlular formation. Lo and behold, a white star full of pure light emerges in the centre. In
complete disbelief, the pacmen are mesmerized. Which of the gestalt laws of perception explain(s)

the appearance of the star in the centre?

 ANS :A,B,D

for Gestalt law of perception visit 

http://graphicdesign.spokanefalls.edu/tutorials/process/gestaltprinciples/gestaltprinc.htm

 Q.38 If the black lines represent cutting lines and dotted pink lines are folding lines, which of the
options correctly represent(s) the opened up surfaces of the solid shown?

 ANS : B,C
 Q.39 Which of the following images belong(s) to Ajanta?

A. H
B. L
C. K and M

D. J and I
 ANS : A,C,D ( except L )

 Q.40 Based on the paintings below, which of the following statements is/are TRUE?

A. These paintings use geometric grids for their construction.

B. All three painting are from Maharashtra.

C. All these paintings draw upon tribal folklore.

D. These paintings are wall murals.

ANS :  C,D 

 Q.41 Which of the following is/are greenhouse gas(es)?

A. Hydrogen Sulphide

B. Carbon Dioxide

C. Chlorine

D. Methane

ANS :B,D 

Q.42 Which of the options represent(s) correctly the opened up surfaces of the solid shown?

 ANS : A,D  

 Q.43 Consider the following text by Edward Shanken:

“By 2000, it had become increasingly apparent that the exclusion and ghettoization confronting the

practice and criticism of new media art and the larger historiography of art and technology required

an explicit suturing strategy. In ‘Art in the Information Age’ (2001) I argued that by ‘interpreting

conceptual art and art-and-technology as reflections and constituents of broad cultural

transformations during the information age’ categorical distinctions can be relaxed, allowing parallels

to be drawn between seemingly diverse theory of systems aesthetics and the notion of software as a

metaphor for art. My analysis of works by Levine, Haacke and Kosuth in ‘Software’ led to the

conclusion that in the information age, ‘meaning and value are not embedded in objects, institutions

or individuals so much as they are abstracted in the production, manipulation and distribution of signs

and information’. Finally, I implicitly applied Burnham’s systems approach to analyse the system by

which art history is written. Using Haacke and Ascott as examples, I claimed that the historicization of

an artist’s work as conceptual art or art and technology ‘says less about their work than it does about

the institutional mechanisms that have created and reinforced categorical distinctions...at the

expense of identifying continuities between them.”

Which of the statements is/are TRUE of the paragraph above?

A. Historicization of an artist’s work speaks only of institutional mechanisms that create and

define categories.

B. Categorical distinctions do not allow parallels to be drawn between seemingly diverse

practices.

C. If software is a metaphor for art, meaning and value are more in the making and distribution

of signs and information.

D. Conceptual art cannot be interpreted as reflections of broad cultural transformations.

ANS : B,C

  

Q.44 The following diagram shows the distribution of population in an apartment building as per

the profession of its residents.

Which of the following is/are correct?

A. Doctors and businessmen combined is less than half of the total residents.

B. About 1/3 of the population is engineers.

C. Engineers and designers combined is about 60% of the residents.

D. Doctors and businessmen combined is more than half of the total residents

 ANS : A,B,C 

Q.45 In which of the following applications is a convex lens used?

A. Peepholes

B. Magnifying glass

C. Microscope

D. Car headlight

ANS : A,B,C,D 

IIT JEE PAPER 2 (B ARCH) PREPARATION GUIDE FOR APTITUDE TEST

  IN ARCHITECTURE APTITUDE TEST  FOR IIT JEE  AND NATA  THE DRAWING AND             FIGURE  RELATED QUESTIONS ARE OF   FOLLOWING TYPES

*  Identifying the correct elevation from the top view.
*  Identifying the correct top view ,front view, side view from the 3 D view.
*  Finding the correct mirror image of the figure.
*  Finding hidden objects.
*  Finding correct view of the 3-D problem figure after the problem figure is opened up .
*  Completing the sequence of the figure.(rotation).
*  Finding the total number of surface of the object given below in the problem.

 These types of questions are very scoring if your concepts are clear.

With examples I will explain how to visualize and solve the problems 

 Q 1  The 3-D problem figure shows a view of an object. Identify the correct front view,
         from amongst the answer figures, looking in the direction of arrow.

ANS                                      we can  find the front view looking in the direction of arrow
 by coloring  the sides in that direction. By observing we can say that   option 2 is correct.

At first glance we can say that option 1 and 3 are incorrect.
option 2 and 4 are close, so be careful in answering.

By practicing these type of questions you can answer it simply by observation even without coloring it.





Q 2   The 3-D problem figure shows a view of an object. Identify the correct TOP view,
         from amongst the answer figures,

 ANS 

                                                          we can  find the top view by coloring  the top surfaces.                                                                            By observing we can say  that  option 2 is correct.

    1 and 2  are nearly same , for correct answer check the                       proportion of the  parts. 

Q 3  The 3-D problem figure shows a view of an object. Identify the correct front view,

        from amongst the answer figures, looking in the direction of arrow.

       

 ANS

 

By coloring in the direction of arrow , we can say that option 2 is correct view.

Always first see the surface that is closer to the arrow and than go farther.
2 and 4 are closer except the elevation of the sloping side.Be careful in that.







Q 4 The problem figure shows the top view of objects. Looking in the direction of arrow, identify the         correct elevation, from amongst the answer figures.
   

ANS 

The pink lines show the edges of the object
that are visible  prominently.
The blue lines shows the edges that are partly visible and partly hidden behind the front objects.

by observing ans 3 is correct.









Q 5      Which one of the answer figures is the correct mirror image of the problem
            figure with respect to X–X ?

       

ANS

to find the mirror image quickly,
mark the points nearer and farther from xx line say point a,b,c and p
there mirror points will be equidistant from xx line on the right side i.e, a',b',c',p'  such that ax=xa' ,bx=xb' , cx=xc' and px=xp'.
similarly you can draw/ observe  the complete figure.
1 is the correct mirror image of the figure.

1 and 4 are closer except the middle part, be careful in answering.

Q 6  One of the following answer figure is hidden in the problem figure in the same size and                       direction. Select the correct one.

ANS                                                

 observation is the only way to solve these type of problems.
mind that hidden figure is in the same size and direction.

1 is the correct answer.

 (my vague idea is to see the figure with half closed eyes ,you         will not believe, it works.)



Q 7   Which one of the answer figures, shows the correct view of the 3-D problem
         figure, after it is opened up ?

     

A 7            correct answer is 3                                                                      

           

                                                           As marked in ans figure check bottom side(in red) and  top side  ( in green)  surfaces                            

                    check the number of surfaces and their proportion also as shown                                                                                                                                                                                                                                                                                                                   















Q 8         Which one of the answer figures will complete the sequence of the three problem figures?

   ANS     By observing we can say that figure is being rotated 45 degree anti clockwise each time.
               The next sequence will be rotated 45 degree anti clockwise having circle on top, and  4 is                      the correct next sequence. 

Q 9        Find the total number of surface of the object given below in the problem.
             

ANS  

                  Count the visible and hidden surfaces as shown in figure .

The correct answer is 18 .