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kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Last visit: 27 Jul 2022
Posts: 706
Given Kudos: 276
Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
GPA: 3.6
16 May 2019, 00:40
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
76% (02:40) correct
24%
(02:37)
wrong
based on 335
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The range of a set of integers: a, b, 5, 7, and 11 is 6 and its median is a. Which of the following can be the value of a×b?
A. 40
B.45
C. 49
D. 50
E. 60
A. 40
B.45
C. 49
D. 50
E. 60
19 May 2019, 19:41
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kiran120680
Since the range is 6, a and b be must be greater than or equal to 5 and less than or equal to 11. Also, since the median is a, the numbers in ascending order, must be {5, 7, a, b, 11} or {5, b, a, 7, 11}.
We see that in the first case, 7^2 ≤ ab ≤ 11^2, i.e., 49 ≤ ab ≤ 121, and in the second case 5^2 ≤ ab ≤ 7^2, i.e., 25 ≤ ab ≤ 49.
Though it seems all answer choices are in either range, we have to remember that a and b are both integers and are members of the set. For example, if ab = 50, we see {a, b} can be {1, 50}, {2, 25} or {5, 10}; however, none of these have both numbers between 7 and 11 (inclusive) in the first case or between 5 and 7 (inclusive) in the second case. So 50 is not the correct answer.
On the other hand, if ab = 49 and {a, b} is {7, 7}, we do have both numbers between 7 and 11 (inclusive) in the first case or between 5 and 7 (inclusive) in the second case. So 49 is the correct answer.
Answer: C
General Discussion
16 May 2019, 13:49
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Range:
11 - 5 = 6 --- OK
Set:
5 - a - 7 - b - 11
Median is a, hence:
5 - 7 - 7 - 7 - 11
7x7 = 49
C
11 - 5 = 6 --- OK
Set:
5 - a - 7 - b - 11
Median is a, hence:
5 - 7 - 7 - 7 - 11
7x7 = 49
C
