By approximately what percent is x greater

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

by Vincen » Mon Oct 02, 2017 10:08 am

By approximately what percent is x greater than 4/5 if (4/5)(x) = 1?

A. 73%
B. 56%
C. 41%
D. 37%
E. 29%

B is the OA.

How can I do this PS question? Should I substitute each percentage in x?

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Source: Beat The GMAT — Problem Solving | Mon Oct 02, 2017 10:08 am

jbryant62: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Nov 23, 2016 4:04 pm; Thanked: 1 times

by jbryant62 » Mon Oct 02, 2017 12:46 pm

Vincen wrote:By approximately what percent is x greater than 4/5 if (4/5)(x) = 1?

A. 73%
B. 56%
C. 41%
D. 37%
E. 29%

B is the OA.

How can I do this PS question? Should I substitute each percentage in x?

In order for the equation to equal 1, X has to be the reciprocal of 4/5. So X is 5/4. Fractions are hidden division problems. therefore 4/5 =.8 and 5/4 =1.25. so percent change is (new value-original)/ original. (1.25-.8)/.8-=.5625 or approx. 56%. Or you could have just divided 1.25/.8= 1.5625 therefore it is 56% greater

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Mon Oct 02, 2017 12:49 pm

If (4/5)x = 1, then x = 5/4

Target question: by what percent is 5/4 greater than 4/5?

Since these fractions easily convert to decimals, that is the easiest way to calculate the difference: By what percent is 1.25 greater than 0.8?

Percent change = (difference)/(original)
Difference = 1.25 - 0.8 = 0.45
(0.45)/(0.8) = 45/80 = 9/16
--> this is slightly more than half. Look at the answer choices. Since only 56 is slightly more than half, we can pick it without doing any further calculation.

The answer is B.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Mon Oct 02, 2017 12:52 pm

jbryant62 wrote: In order for the equation to equal 1, X has to be the reciprocal of 4/5. So X is 5/4. Fractions are hidden division problems. therefore 4/5 =.8 and 5/4 =1.25. so percent change is (new value-original)/ original. (1.25-.8)/.8-=.5625 or approx. 56%. Or you could have just divided 1.25/.8= 1.5625 therefore it is 56% greater

Since you won't have a calculator on the Quant section of the GMAT, it's not advisable to hand-calculate division such as 1.25/0.8. That would eat up a lot of valuable time. First, estimate. Then, do calculations only if there are answer choices that are too close together; this was not the case here.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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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

by Brent@GMATPrepNow » Mon Oct 02, 2017 1:54 pm

Once we know that we must determine the percent change from 0.8 to 1.25, might also recognize that 0.4 is 50% of 0.8
So, 1.2 is 50% greater than 0.8 (aside: 0.8 + 0.4 = 1.2)
So, 1.25 must be a LITTLE BIT MORE than 50% greater than 0.8
Check the answer choices....only answer choice B (56%) is a bit more than 50%

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sat Oct 07, 2017 3:18 pm

Vincen wrote:By approximately what percent is x greater than 4/5 if (4/5)(x) = 1?

A. 73%
B. 56%
C. 41%
D. 37%
E. 29%

B is the OA.

How can I do this PS question? Should I substitute each percentage in x?

Hi Vicen,
Let's take a look at your question.

We can find value of x using the equation:
(4/5)(x) = 1
x = 5/4
x = 1.25

The question states,
"By approximately what percent is x greater than 4/5"
Since x = 1.25 and 4/5 = 0.8
Therefore, we need to find,
By approximately what percent is 1.25 greater than 0.8
It means we need to find the percent change.
Original value = 0.8
New Value = 1.25

Percent Change = [(New Value - Original Value) / Original Value ] * 100%

Percent Change = [(1.25 - 0.8)/0.8] * 100%
Percent Change = [0.45/0.8] * 100%
Percent Change = 0.5625 * 100%
Percent Change = 56.25%
Which is approximately equal to 56%.

Therefore, Option B is correct.

I am available if you'd like any followup.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: By approximately what percent is x greater

by Scott@TargetTestPrep » Fri Jan 24, 2020 9:38 am

Vincen wrote: ↑
Mon Oct 02, 2017 10:08 am
By approximately what percent is x greater than 4/5 if (4/5)(x) = 1?

A. 73%
B. 56%
C. 41%
D. 37%
E. 29%

B is the OA.

How can I do this PS question? Should I substitute each percentage in x?

Solving for x, we have:

x = 5/4

Thus:

(5/4 - 4/5) / 4/5 x 100 = (1.25 - 0.8)/0.8 x 100 ≈ 0.56 = 56%

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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