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- 1. DATA INTERPRETATION 1 http://nov15.wordpress.com/ Presents DI & LR For CAT 2009
- 2. DATA INTERPRETATION
- 3. INTRODUCTION
- 4. 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
- 5. 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 +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.
- 6. 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.
- 7. 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
- 8. SOLUTION Let’s check (c) (c) 17<B<20<D<E 17 + 18 = 35 So, 17<18<20<D<E Examine all their combinations : 17+18 = 35 17+20 = 37 18+20 = 38 (wrong) So, (c) is wrong, correct answer is (b)
- 9. 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.
- 10. 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
- 11. 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
- 12. 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
- 13. 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
- 14. 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
- 15. 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.
- 16. LET ME KNOW!! If you liked this presentation, do comment on http://nov15.wordpress.com or write to Nicky at nickyswetha20@yahoo.com
- 17. THANK YOU

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