DATA INTERPRETATION 1

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CAT 2009CAT 2009

DATA INTERPRETATION

INTRODUCTION

TYPE 1 : AVERAGES TYPE

Questions are of the following type :

A rural child specialist has to determine the weight of different ages. He knows from past experience that each child would weight less than 30 kg and each of them would have different weights. Unfortunately, the scale in the village could measure only weights above 30 kgs. So, he measured the children in pairs and the weights are: 35,36,37,39,40,41,42,45,46 & 47 kgs. He however forgot to note down their names. What is the weight of the lightest child? (XAT 2009)

A) 15 kg B) 16 kg C) 17 kg D) 18 kg E) 20 kg

SOLUTION Let us assume there are 5 children such that

A<B<C<D<E Now, A+B/A+C/A+D/A+E would be the possible

combinations. So, each child is weghed 4 times.

So, 4(A+B+C+D+E)=

35+36+37+39+40+41+42+45+46 +47A+B+C+D+E = 408/4 = 102

We know, A+B = min = 35, D+E = max = 47

(35)+C+(47) = 102 => C = 20 kgs.

SOLUTION

So, we have the weights as A<B< 20< D< E

Examining the options, we can rule out (e) as, if 20 was least weight, A and B cannot be lesser.

Also, 18 + 17 = 35, so 18 cannot be least weight! So, (d) is out.

Also, 15 + 20 = 35, but 20 is supposed to be 3rd largest. So, (a) is ruled out.

SOLUTION

Now, using (b) and (c)

(b) 16 < B < 20 < D < E So, B should be 35 – 16 = 19

Now, we get 16 < 19 < 20 Examine all their combinations : 16+19 = 35 16+20 = 3619+20 = 39

SOLUTION Let’s check (c)

(c) 17<B<20<D<E 17 + 18 = 35 So, 17<18<20<D<EExamine all their combinations : 17+18 = 35 17+20 = 3718+20 = 38 (wrong)

So, (c) is wrong, correct answer is (b)

SLIGHT MODIFICATION There are 6 students in a class, where marks are arranged

as A>B>C>D>E>F (all integers)

Their teachers gave sum of marks of 5 of them as follows :

But, one of them is lying. Using the above info, answer the following questions.

Teacher Marks

English 232

Math 238

Bio 244

Geo 245

Marathi 250

Hindi 256

History 235

SLIGHT MODIFICATION

1. What is the difference between the highest and lowest total score?

a) 21 b) 24 c) 18 d) 27 e) none

2. What is the second highest score? a) 55 b) 56 c) 57 d) 55 or 56 e) none

3. What is the least possible score?a) 34 b) 35 c) 36 d) 37 e) none

4. If sum of at least 2 scores is 80, which can be sum of 2 or more scores?

a) 93 b) 104 c) 110 d) 102 e) none

SOLUTION

No. of combinations = 6C5 = 6 combinations

But, we are given 7 values. So 1 value is redundant.

Now, let us consider the redundant value as X

5(A+B+C+D+E+F) + X = 232+238+244+245+250+256+235 = 1700

So, A+B+C+D+E = (1700 – X)/5As all the marks are integers, 1700 – X must be

divisible by 5.

This will happen only if X is ending with 5 or 0

SOLUTION

So, only geography, marathi or hindi teachers can be lying.

Consider Geo teacher is lying. Then,

(1700 – 245) / 5 = 291Now, we obtain the various marks as, (A+B+C+D+E) – (A+B+C+D) = EIe., 291 – 232 = 59 291 – 250 = 41291 – 238 = 53 291 – 256 = 35291 – 244 = 47 291 – 235 = 56

SOLUTION

Arrange such that A>B>C>D>E The marks can be tabulated for each lying

teacher as follows.

Teacher Total A B C D E F

Geo (1700-245)/5 = 291 59 56 53 47 41 35

Marathi (1700-250)/5 = 290 58 55 52 46 40 34

Hindi (1700-235)/5 = 293 61 58 55 49 43 37

SOLUTION

Answering the questions : 1. What is the difference between the highest

and lowest total score? a) 21 b) 24 c) 18 d) 27 e) none

Solution: In each case 59-35 = 24 | 58-34 = 24 | 61-37 = 24

2. What is the second highest score? a) 55 b) 56 c) 57 d) 55 or 56 e) none

Solution: From each case, we get second highest scores as

56,55 and 58

SOLUTION

3. What is the least possible score?a) 34 b) 35 c) 36 d) 37 e) none

Solution: Least possible score is present in case with

marathi teacher lying -> 34

4. If sum of at least 2 scores is 80, which can be sum of 2 or more scores?

a) 93 b) 104 c) 110 d) 102 e) none Solution:

Sum of least scores = 80, in case with Hindi Teacher lying. Here we get, 55 + 49 = 104. and no other combination.

EXERCISE

Visit the following link for exercises on this type of Data Interpretation Problems.

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