If $a \geq 30$ and $b \leq 15$, then which of the following must also be true?

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BTGmoderatorLU: Moderator; Posts: 2558; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Aug 17, 2020 12:55 pm

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Source: Princeton Review

If $a \geq 30$ and $b \leq 15$, then which of the following must also be true?

A. $a - b \leq 45$
B. $a - b \leq 15$
C. $a - b \geq 15$
D. $a + b \leq 45$
E. $a + b \geq 45$

The OA is C

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Source: Beat The GMAT — Problem Solving | Mon Aug 17, 2020 12:55 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: If $a \geq 30$ and $b \leq 15$, then which of the following must also be true?

by Brent@GMATPrepNow » Wed Aug 19, 2020 4:43 am

BTGmoderatorLU wrote: ↑
Mon Aug 17, 2020 12:55 pm
Source: Princeton Review

If $a \geq 30$ and $b \leq 15$, then which of the following must also be true?

A. $a - b \leq 45$
B. $a - b \leq 15$
C. $a - b \geq 15$
D. $a + b \leq 45$
E. $a + b \geq 45$

The OA is C

In many of the other choices, we have -b (subtract b)

So let's take: b ≤ 15
And multiply both sides by -1 to get: -b ≥ -15 [aside: Since I multiplied both sides of the inequality by a NEGATIVE number, I had to REVERSE the direction of the inequality symbol]

So we now have the following:
a ≥ 30
-b ≥ -15

If we ADD the two inequalities we get: a + (-b) ≥ 30 + (-15)
Simplify to get: a - b ≥ 15

Answer: C

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If $a \geq 30$ and $b \leq 15$, then which of the following must also be true?

by Scott@TargetTestPrep » Sat Aug 22, 2020 11:00 am

BTGmoderatorLU wrote: ↑
Mon Aug 17, 2020 12:55 pm
Source: Princeton Review

If $a \geq 30$ and $b \leq 15$, then which of the following must also be true?

A. $a - b \leq 45$
B. $a - b \leq 15$
C. $a - b \geq 15$
D. $a + b \leq 45$
E. $a + b \geq 45$

The OA is C

Solution:

If a = 31 and b = 1, then a - b = 30 and a + b = 32. We see that we can eliminate choices B and E from the correct answer. Now, if a = 51 and b = 1, then a - b = 50 and a + b = 52. We see that we can also eliminate choices A and D from being the correct answer. Therefore, the correct answer, after the process of elimination, is C.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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