If a,b, and c are positive integers with at least one of

Question

If a,b, and c are positive integers with at least one of the three equal to 7, is the median of the set {a,b,c} greater than 7?

(1) a<7
(2) c>7

New question

amanvermagmat · Accepted Answer

At least one of the three = 7. (1) a < 7 So at least one integer = 7, and one integer < 7. If third integer = 7, then since two integers = 7, median of these three = 7 If third integer < 7, then since two integers < 7, median of these three < 7 If third integer > 7, then the median of these three = 7 So the median will either be = 7 or < 7, but never > 7. So this gives NO as an answer to the question asked. Sufficient. (2) c > 7 So at least one integer = 7, and one integer > 7 If third integer = 7, then since two integers = 7, median of these three = 7 If third integer > 7, then since two integers > 7, median of these three > 7 So the median might be = 7 or greater than 7 also. This doesnt give a definite YES or NO to the question asked. Not Sufficient. Hence A answer

EgmatQuantExpert · Answer

Solution

Given:

• a, b, and c are positive integers.
• At least one of a, b, and c is 7.

To find:

• Is the median of the set {a,b,c} greater than 7?

Statement-1:   “a<7 “

If a is less than 7 then there can be three cases in which numbers will be arranged.
 • a, 7, greater than 7
 o In this case, median is 7.

• a, (less than 7 and greater than a), 7
 o In this case, median is certainly less than 7.

• Less than a, a, 7
 o In this case, median is a which is less than 7.

In all the cases median is less than 7. 
Hence, Statement 1 alone is sufficient to answer the question.

Statement-2:   “c>7 “

If c is greater than 7 then there can be some cases in which numbers will be arranged.

• 7, c, greater than c
 o In this case, median is c which is greater than 7.

• Less than 7, ,7 c, 
 o In this case, median is 7.

Since we do not have a unique answer from the two cases, we do not need to check for rest of the cases.
Statement 2 alone is not sufficient to answer the question.

Hence, the correct answer is option A.

Answer: A

push12345 · Answer

Chetan2u

Could you please check OA for same
I also got answer as A but OA given is D

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chamarts · Answer

I think the definition of median is middle number. You can conclusively say 7 of both I and II are provided

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vishuvashishth · Answer

chetan2u 
While posting solutions,Everyone has assumed this series to be an evenly spaced series or set. However, this is not mentioned in the question stem. Does this conclusively apply to gmat questions too ? Please suggest !

ymba2020 · Answer

One simple way to go ahead with this problem would be :

To prove that the median of set{a,b,c} is greater than 7, when given that one of the number is equal to 7, we need 2 numbers to be greater than 7.

Statement 1 says exactly the same thing. It says that there is one number that is less than 7 and the other equal to 7. So whatever may be the value of the third variable, the median is never going to exceed 7.

Hope this helps!

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If a,b, and c are positive integers with at least one of

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