If a is an integer greater than 4 but less than 21...

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

If a is an integer greater than 4 but less than 21...

by AAPL » Tue Nov 28, 2017 6:30 pm

If a is an integer greater than 4 but less than 21 and b is an integer greater than 14 but less than 31, what is the range of a/b?

A. 2/3
B. 1/2
C. 5/6
D. 1
E. 7/6

The OA is E.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Nov 28, 2017 6:30 pm

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Wed Nov 29, 2017 9:33 am

AAPL wrote:If a is an integer greater than 4 but less than 21 and b is an integer greater than 14 but less than 31, what is the range of a/b?

A. 2/3
B. 1/2
C. 5/6
D. 1
E. 7/6

The OA is E.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

This question could have been worded a little more clearly - in effect, it seems to be asking us to find the range of possible values for a/b, or rather (greatest a/b) - (smallest a/b)

Greatest a/b: Here we'd want to maximize a and minimize b. Max possible a: 20. Min possible b: 15. Max a/b = 20/15

Smallest a/b: Here's we'd want to minimize a and maximize b. Min possible a: 5. Max possible b: 30. Min a/b = 5/30

Difference: 20/15 - 5/30 = 40/30 - 5/30 = 35/30 = 7/6. The answer is E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Oct 07, 2019 6:56 pm

AAPL wrote:If a is an integer greater than 4 but less than 21 and b is an integer greater than 14 but less than 31, what is the range of a/b?

A. 2/3
B. 1/2
C. 5/6
D. 1
E. 7/6

The OA is E.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

A positive fraction is maximized when the numerator is as large as possible and the denominator is as small as possible. Thus, the maximum value of a/b is 20/15 = 4/3.

Similarly, a positive fraction is minimized when the numerator is as small as possible and the denominator is as large as possible; thus, the minimum value of a/b is 5/30 = 1/6.

Therefore, the range of values of a/b is 4/3 - 1/6 = 8/6 - 1/6 = 7/6.

Answer: E

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