Example Case 7
Read the following and answer the questions that follow
Five women decided to go shopping to M.G. Road, Bangalore. They arrived at the designated meeting place in the following order: 1. Archana, 2. Chellamma, 3. Dhenuka, 4. Helen, and 5. Shahnaz. Each woman spent at least Rs. 1000. Below are some additional facts about how much they spent during their shopping spree.
i. The woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193.
ii. One woman spent Rs. 1340 and she was not Dhenuka.
iii. One woman spent Rs. 1378 more than Chellamma.
iv. One woman spent Rs. 2517 and she was not Archana.
v. Helen spent more than Dhenuka.
vi. Shahnaz spent the largest amount and Chellamma the smallest.
[CAT 2003L]
16) What was the amount spent by Helen?
(1) Rs. 1193
(2) Rs. 1340
(3) Rs. 2234
(4) Rs. 2517
17) Which of the following amounts was spent by one of them?
(1) Rs. 1139
(2) Rs. 1378
(3) Rs. 2571
(4) Rs. 2718
18) The woman who spent Rs. 1193 is
(1) Archana
(2) Chellamma
(3) Dhenuka
(4) Helen
We’ll use the first letter of the name of every woman (A, C, D, H and S) for Archana, Chellamma, Dhenuka, Helen and Shahnaz respectively.
Note: The arrow mark used in the notes is to mention who comes after who. For example if C came before D, it would be like C D.
The order in which they arrived is also given. We need to match the amount spent by each woman. We’ll form a table with each woman in different column in the order they arrived.
We’ve got four different amounts spend by these women from the clues itself.
Now we are left with two cases pertaining to the money spend by C. In statement 6) it is given that then amount spent by C is the smallest.
Case 1
As C is the smallest, we shall take the smallest of the amounts we got from the clues as the amount spent by C i.e., 1193.
When we add 1378 with C's spend as per statement 3, then X = 2571 which is the max of all of them. So X has to be S over here. So the min and max in this case is 1193 and 2517.
Case 2
Now we’ll take the max value from the four values we have, i.e., 2517. If the max is 2517, then the min cannot be 1193. If the min is 1193, then 1193 + 1378 would result in 2571 which is greater than 2517. So for C to be min in this case, X should be the max as we are adding 1378, which is a very big number, with C’s value. If we look at the difference between the min and max of the four values, 2517 - 1193 = 1324. So the maximum difference allowed if 1193 and 2517 are the min and max is 1324, but there is already a difference of 1378 which is bigger than 1324. Therefore 2517 and 1193 cannot be max and min at the same time. So now in this case as 2517 is the max, then min should be 2517 - 1378 = 1139. So the min and max in this case is 1139 and 2517.
So let us check with Case 1 and see whether this is satisfying the conditions.
In this case the min and max is 1193 and 2571.
Statement 1) says that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. So the only person before the person spent 1193 is A. Therefore A has to be 2234.
Now we are left with the amounts 1340 and 2517.
Statement 2) says that D is not the person who spent 1340. So D has to be 2517. Then H has to be 1340.
Now this doesn’t satisfy statement 5), H > D. Therefore case 1 is not true as it is not satisfying all conditions.
Now let us check with case 2. In this case the min and max is 1139 and 2517.
The amounts not used are 1193,1340 and 2234. The smallest among these three is 1193. H cannot be 1193 as H must be greater than D.
Statement 1) says that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. As A is the first person to arrived there, A cannot be the person who spent 1193 as this would not satisfy statement 1). Therefore D must be the person who spent 1193.
Now the two persons left to be filled are A and H and the amounts left are 2234 and 1340. To satisfy statement 1, A must be the person who spent 2234. Therefore H spent 1340.
This case satisfies all conditions, and 1340 is the correct choice.
Answer: (2) Rs. 1340
17)
The table is as follows, and the correct choice is 1139, as none of the other amounts are spent.
Answer: (1) Rs. 1139
18)
Based on the table, it is Dhenuka.
Answer: (3) Dhenuka
Answer:
16) (2) Rs. 1340
17) (1) Rs. 1139
18) (3) Dhenuka
Five women decided to go shopping to M.G. Road, Bangalore. They arrived at the designated meeting place in the following order: 1. Archana, 2. Chellamma, 3. Dhenuka, 4. Helen, and 5. Shahnaz. Each woman spent at least Rs. 1000. Below are some additional facts about how much they spent during their shopping spree.
i. The woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193.
ii. One woman spent Rs. 1340 and she was not Dhenuka.
iii. One woman spent Rs. 1378 more than Chellamma.
iv. One woman spent Rs. 2517 and she was not Archana.
v. Helen spent more than Dhenuka.
vi. Shahnaz spent the largest amount and Chellamma the smallest.
[CAT 2003L]
16) What was the amount spent by Helen?
(1) Rs. 1193
(2) Rs. 1340
(3) Rs. 2234
(4) Rs. 2517
17) Which of the following amounts was spent by one of them?
(1) Rs. 1139
(2) Rs. 1378
(3) Rs. 2571
(4) Rs. 2718
18) The woman who spent Rs. 1193 is
(1) Archana
(2) Chellamma
(3) Dhenuka
(4) Helen
Case Solution
16)We’ll use the first letter of the name of every woman (A, C, D, H and S) for Archana, Chellamma, Dhenuka, Helen and Shahnaz respectively.
Note: The arrow mark used in the notes is to mention who comes after who. For example if C came before D, it would be like C D.
The order in which they arrived is also given. We need to match the amount spent by each woman. We’ll form a table with each woman in different column in the order they arrived.
We’ve got four different amounts spend by these women from the clues itself.
Now we are left with two cases pertaining to the money spend by C. In statement 6) it is given that then amount spent by C is the smallest.
Case 1
As C is the smallest, we shall take the smallest of the amounts we got from the clues as the amount spent by C i.e., 1193.
When we add 1378 with C's spend as per statement 3, then X = 2571 which is the max of all of them. So X has to be S over here. So the min and max in this case is 1193 and 2517.
Case 2
Now we’ll take the max value from the four values we have, i.e., 2517. If the max is 2517, then the min cannot be 1193. If the min is 1193, then 1193 + 1378 would result in 2571 which is greater than 2517. So for C to be min in this case, X should be the max as we are adding 1378, which is a very big number, with C’s value. If we look at the difference between the min and max of the four values, 2517 - 1193 = 1324. So the maximum difference allowed if 1193 and 2517 are the min and max is 1324, but there is already a difference of 1378 which is bigger than 1324. Therefore 2517 and 1193 cannot be max and min at the same time. So now in this case as 2517 is the max, then min should be 2517 - 1378 = 1139. So the min and max in this case is 1139 and 2517.
So let us check with Case 1 and see whether this is satisfying the conditions.
In this case the min and max is 1193 and 2571.
Statement 1) says that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. So the only person before the person spent 1193 is A. Therefore A has to be 2234.
Now we are left with the amounts 1340 and 2517.
Statement 2) says that D is not the person who spent 1340. So D has to be 2517. Then H has to be 1340.
Now this doesn’t satisfy statement 5), H > D. Therefore case 1 is not true as it is not satisfying all conditions.
Now let us check with case 2. In this case the min and max is 1139 and 2517.
The amounts not used are 1193,1340 and 2234. The smallest among these three is 1193. H cannot be 1193 as H must be greater than D.
Statement 1) says that the woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193. As A is the first person to arrived there, A cannot be the person who spent 1193 as this would not satisfy statement 1). Therefore D must be the person who spent 1193.
Now the two persons left to be filled are A and H and the amounts left are 2234 and 1340. To satisfy statement 1, A must be the person who spent 2234. Therefore H spent 1340.
This case satisfies all conditions, and 1340 is the correct choice.
Answer: (2) Rs. 1340
17)
The table is as follows, and the correct choice is 1139, as none of the other amounts are spent.
Answer: (1) Rs. 1139
18)
Based on the table, it is Dhenuka.
Answer: (3) Dhenuka
Answer:
16) (2) Rs. 1340
17) (1) Rs. 1139
18) (3) Dhenuka