What number is 23 more than three-fourth of itself?

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Thu Jun 14, 2018 1:10 am

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What number is 23 more than three-quarters of itself?

A. 82
B. 92
C. 108
D. 116
E. 124

The OA is the option B.

How should I solve this PS question? Should I prove each option or should I set an equation that solves the problem? What is the best way? Thanks for your help.

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Source: Beat The GMAT — Problem Solving | Thu Jun 14, 2018 1:10 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Thu Jun 14, 2018 2:52 am

Hello Vjesus12.

We can set equation that represents the problem as follows: $$x=23+\frac{3}{4}x\ $$ $$x-\frac{3}{4}x=23$$ $$\frac{1}{4}x=23\ $$ $$x=92.$$ Therefore, the correct answer is the option B.

I hope it helps you. <i class="em em-smiley"></i>

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Jun 14, 2018 5:45 pm

Hi VJesus12,

We're asked for the number that is 23 more than three-quarters of itself. Many Test Takers would likely solve this question Algebraically (which is fine), but you can also solve it with a little Arithmetic and TESTing THE ANSWERS.

To start, if a number is 23 more than 3/4 of itself, then that difference of 23 must represent the 'missing 1/4' of that value. Thus, we're really asked "23 is 1/4 of what number?"

You probably already know that 25 is exactly 1/4 of 100, so 23 must be 1/4 of some number that is LESS than 100. You might also recognize that dividing 82 by 4 will lead to a NON-integer; adding 23 to a non-integer would end with a non-integer (and none of the answers are non-integers) so that's not going to be the answer. There's only one answer remaining.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Sun Jun 17, 2018 7:08 pm

VJesus12 wrote:What number is 23 more than three-quarters of itself?

A. 82
B. 92
C. 108
D. 116
E. 124

We can let x = the actual number. Since the number is 23 more than 3/4 of itself, we can create the following equation to determine x.

x = 23 + (3/4)x

1/4(x) = 23

x = 92

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[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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