Percentage Conundrum

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BlueDragon2010: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Tue Mar 31, 2009 11:19 amFollowed by: 1 member

by BlueDragon2010 » Wed Jun 09, 2010 10:12 pm

Positive integer y is 50% of 50% of positive integer x, and y percent of x equals 100. What is the value of x?

A) 50
B) 100
C) 200
D) 1,000
E) 2,000

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Source: Beat The GMAT — Problem Solving | Wed Jun 09, 2010 10:12 pm

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Wed Jun 09, 2010 10:15 pm

This question is from the the OG12 Diagnostic test, # 12. The OA is C. Two detailed solutions and take-aways lessons are attached. People who cannot see attachments click here.

-Patrick

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OG12 Solutions-T012.pdf: (80.26 KiB) Downloaded 277 times

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The Jock: Master | Next Rank: 500 Posts; Posts: 207; Joined: Mon Oct 06, 2008 12:22 amFollowed by: 3 members; Location: India; Thanked: 5 times

by The Jock » Wed Jun 09, 2010 11:15 pm

y is 50% of 50% of positive integer x = y is 1/2 of 1/2 of x => y = 1/4(x) ------(1)
y percent of x equals 100 = y/100 * x = 100 => xy = 1000 ------(2)
from equation 1 and 2
x*(1/4x) = 1000
x^2 = 4*1000
X^2 = 4000
X = square root of 4000
x = 200
so the answer is C

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Wed Jun 09, 2010 11:51 pm

If x = 100a
then y = 25a ( y 1/2 of 1/2 of x or 1/4 of x)
25a % of x i.e (25a/100) * 100a = 100

25aÂ² = 100

a = + - 2

since x is + so IMO C

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

by outreach » Thu Jun 10, 2010 11:30 am

y=(1/2)*(1/2)*x - 1
(y/100)*x=100 - 2

sub value of y from eq1 in eq2
x=200

BlueDragon2010 wrote:Positive integer y is 50% of 50% of positive integer x, and y percent of x equals 100. What is the value of x?

A) 50
B) 100
C) 200
D) 1,000
E) 2,000

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https://amarnaik.wordpress.com
MBA blog
https://amarrnaik.blocked/

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singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Sun Jun 13, 2010 6:16 am

The Jock wrote:y is 50% of 50% of positive integer x = y is 1/2 of 1/2 of x => y = 1/4(x) ------(1)
y percent of x equals 100 = y/100 * x = 100 => xy = 1000 ------(2)
from equation 1 and 2
x*(1/4x) = 1000
x^2 = 4*1000
X^2 = 4000
X = square root of 4000
x = 200
so the answer is C

Jock...there is a correction/ typo in your working, though your answer is correct.

xy= 10,000 (y/100*x=100), {also 100* 100=10000}....(1)

x*(1/4x) = 10000
x^2 = 4*10000
X^2 = 40000
X = square root of 40000
x = 200

Thanks, Preet.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jun 13, 2010 1:50 pm

If you struggle with percentages -- and even if you don't -- you might find it easier simply to try out the answers in order to determine which is correct.

Here's why trying out the answers will work. The question asks for a specific amount: the value of x. We know that the value of x has to be one of the answer choices. So we can just try them all out until we find the one that works. Some words of wisdom:

Whenever a PS question asks for a specific amount, consider trying out the answers in order to determine which is correct.

When you're trying out the answer choices, start with the one right in the middle (normally answer choice C).

If the answer right in the middle works, then it's the correct answer.
If the answer right in the middle is too big, you can eliminate both it and the answers that are even larger, and try those that are smaller.
If the answer right in the middle is too small, you can eliminate both it and the answers that are even smaller, and try those that are larger.

Starting with the middle answer choice can help you to eliminate three answer choices at once. Remember this rule:

Start with C and cancel three.

So let's start with answer choice C:

If x = 200, then y = (50/100)(50/100)(200) = 50.
Does y percent of x equal 100?
Yes, because 50 percent of 200 equals 100.
So answer choice C works!

See how easy?

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Resp007: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Sat Aug 31, 2013 1:29 pmFollowed by: 1 member; Thanked: 2 times; GMAT Score:680

by Resp007 » Mon Sep 02, 2013 9:40 am

GMATGuruNY wrote:If you struggle with percentages -- and even if you don't -- you might find it easier simply to try out the answers in order to determine which is correct.

Here's why trying out the answers will work. The question asks for a specific amount: the value of x. We know that the value of x has to be one of the answer choices. So we can just try them all out until we find the one that works. Some words of wisdom:

Whenever a PS question asks for a specific amount, consider trying out the answers in order to determine which is correct.

When you're trying out the answer choices, start with the one right in the middle (normally answer choice C).

If the answer right in the middle works, then it's the correct answer.
If the answer right in the middle is too big, you can eliminate both it and the answers that are even larger, and try those that are smaller.
If the answer right in the middle is too small, you can eliminate both it and the answers that are even smaller, and try those that are larger.

Starting with the middle answer choice can help you to eliminate three answer choices at once. Remember this rule:

Start with C and cancel three.

So let's start with answer choice C:

If x = 200, then y = (50/100)(50/100)(200) = 50.
Does y percent of x equal 100?
Yes, because 50 percent of 200 equals 100.
So answer choice C works!

See how easy?

Hi,
So here's how I approached the question. I think there is something I am missing, can you help please?

For percentage questions, I usually take 100 as starting number because it solved many problems easily.

So here I took, x = 100, so, y = 50% of 50% of 100 = 25....(equation 1).
and since y% of x = 100 as per second information, so if I put the data from 1st equation,
I get 25% of 100 = 100, which is incorrect;
So to make left hand as 100 somehow (remember, I assumed X) I'll multiply X by 4,
so when now X = 400, its 50% * 50% = 100 = Y, and 100% of X = 100, which still is incorrect.

There has to be another way than the way mentioned, I mean try and not use pen and understand and solve mentally?

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GMAT/MBA Expert

[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] » Mon Sep 02, 2013 1:43 pm

Hi Resp007,

The GMAT tests a variety of skills, including a Test Taker's flexibility when it comes to answering questions. This is why there's usually several approaches to answer any particular question. This is also why 90% of Test Takers can't score above a 700 (because they're inflexible).

You can choose to attempt a question such as this in any way that you choose. However, here's how you have to measure "success":

1) Did you get the question correctly?
2) Was your way the fastest way possible to do so?

One final note, and I only mention it because of how you ended your post... not using a pen and doing the work in your head will KILL YOU on this Test. Maybe not early on and maybe not on super easy questions, but it WILL keep you from getting the score that you want. So, be flexible and write EVERYTHING down.

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

Contact Rich at [email protected]

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