If there is a least integer that satisfies the inequality 9/x> 2, what is that least integer?

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu Mar 19, 2020 5:22 am

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If there is a least integer that satisfies the inequality 9/x ≥ 2, what is that least integer?

A. 0
B. 1
C. 4
D. 5
E. There is not a least integer that satisfies the inequality.

Answer: B
Source: Official Guide

Source: Beat The GMAT — Problem Solving | Thu Mar 19, 2020 5:22 am

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Re: If there is a least integer that satisfies the inequality 9/x> 2, what is that least integer?

by Brent@GMATPrepNow » Sat Mar 21, 2020 5:54 am

BTGModeratorVI wrote: ↑
Thu Mar 19, 2020 5:22 am
If there is a least integer that satisfies the inequality 9/x ≥ 2, what is that least integer?

A. 0
B. 1
C. 4
D. 5
E. There is not a least integer that satisfies the inequality.

Answer: B
Source: Official Guide

If 9/x is greater than 2, we know that x is POSITIVE

Since x is POSITIVE, we can eliminate answer choice A.
At this point, we can test values, starting with the smallest possible value.

B) 1
If x = 1, our inequality becomes 9/1 ≥ 2, which is TRUE
Done!

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If there is a least integer that satisfies the inequality 9/x> 2, what is that least integer?

by Scott@TargetTestPrep » Sat Mar 21, 2020 3:09 pm

BTGModeratorVI wrote: ↑
Thu Mar 19, 2020 5:22 am
If there is a least integer that satisfies the inequality 9/x ≥ 2, what is that least integer?

A. 0
B. 1
C. 4
D. 5
E. There is not a least integer that satisfies the inequality.

Answer: B
Source: Official Guide

If x is negative or 0, then 9/x is either negative or undefined, respectively, which will never be greater than or equal to 2. However, if x = 1, then 9/1 = 9 is greater than (or equal to) 2. So the least integer x can be is 1.

Answer: B

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