M36-58

Question

Ten slips of paper, numbered 1 through 10, are placed in a bag. If three slips are chosen at random from the bag without replacement and one of the slips chosen is numbered 7, what is the sum of numbers on the three chosen slips of paper?

(1) The sum of two of the numbers chosen is 16.

(2) The sum of two of the numbers chosen is 14.

(1) The sum of two of the numbers chosen is 16.
 
(2) The sum of two of the numbers chosen is 14.

Bunuel · Answer

Official Solution:

Ten slips of paper, numbered 1 through 10, are placed in a bag. If three slips are chosen at random from the bag without replacement and one of the slips chosen is numbered 7, what is the sum of the numbers on the three chosen slips of paper? 
 
(1) The sum of two of the numbers chosen is 16.
 
If one of those two numbers is 7, then another is 9 and the third number can be any other remaining integers. So, the sum can take more than one value. Not sufficient.
 
(2) The sum of two of the numbers chosen is 14.
 
7 cannot be among those two numbers because in this case another number would also had to be 7, which cannot be the case because the three numbers chosen must be distinct (we are choosing from distinct numbers without replacement). Thus, 7 is the third number and the sum is 14 + 7 = 21. Sufficient.

Answer: B

Tkins · Answer

This makes no sense. If numbered 1-10, then 10 and 6 could be chosen making choice A also possible.

Bunuel · Answer

It makes perfect sense if you read carefully. We are told that one of the chosen numbers is 7. Statement (1) says the sum of two of the numbers chosen is 16.

Case 1:  The three chosen numbers could be 7, 9, and any other number, say 1 (the sum of two of the numbers is 16: 7 + 9 = 16). Thus, the sum of the numbers could be 1 + 7 + 9 = 17.
 
Case 2:  The three chosen numbers could be 7, 10, and 6 (the sum of two of the numbers is 16: 6 + 10 = 16). Thus, the sum of the numbers could be 6 + 7 + 10 = 23.

There are many other cases possible.

We have two different answers. Hence, (1) is not sufficient.

Teriakuk · Answer

I didn’t find any of the offered explanations sufficient (pun-intended), and thought I’d add my approach in case it helped anyone understand this DI question a tad bit more...

1) The first statement alludes to any of the three chosen slips adding up to 16 (which two is unspecified). Thus, if the slips chosen are:
 x, 7, y,

x+y=16, x+7=16 or 7+y=16

Many pairs of numbers could satisfy each equation, making this statement insufficient.

2) The second insinuates any of the three chosen slips add up to 14 (which two is unspecified). Thus, if the slips chosen are: 
 a, 7, b

a+b=14, a+7=14 or 7+b=14
a=b=7

Hence, the second is indeed sufficient.

This leads us to B as the correct answer, as stated by the experts above 😇

ankitksingh · Answer

I like the solution - it’s helpful.

M36-58

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