Data Interpretation

DATA INTERPRETATION 1

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DI & LR For CAT 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


So, 4(A+B+C+D+E)= 35+36+37+39+40+41+42+45+46 +47 A+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


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 = 36 19+20 = 39

SOLUTION 

Let’s check (c)

(c) 17
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 :



Teacher

Marks

English

232

Math

238

Bio

244

Geo

245

Marathi

250

Hindi

256

History

235

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

SLIGHT MODIFICATION What is the difference between the highest and lowest total score? a) 21 b) 24 c) 18 d) 27 e) none 4.

What is the second highest score? a) 55

5.

What is the least possible score? a) 34

6.

b) 56c) 57 d) 55 or 56 e) none b) 35 c) 36 d) 37 e) none

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)/5 As 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 = 291 Now, we obtain the various marks as, (A+B+C+D+E) – (A+B+C+D) = E Ie., 291 – 232 = 59 291 – 250 = 41 291 – 238 = 53 291 – 256 = 35 291 – 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 : 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 5.

= 24 | 58-34 = 24 | 61-37 = 24

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 1.

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



Solution: 

3.

Least possible score is present in case with marathi teacher lying -> 34

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.

http://nov15.wordpress.com/?attachment_id=89

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