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GRE Math Challenge #104- x > 0

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sandy
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GRE Math Challenge #104- x > 0 [#permalink] New post   09 May 2015, 11:22
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Question Stats:

84% (01:00) correct 15% (01:13) wrong based on 170 sessions

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x>0


Quantity A
Quantity B
(590+x)800
(600+x)790



• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
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B
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Re: GRE Math Challenge #104 [#permalink] New post   12 May 2015, 08:30
sandy wrote:
x > 0

Quantity A: (590+x)/800
Quantity B: (600+x)/790


Two nice rules concerning fractions with positive numerators and denominators:
1) Making a numerator bigger makes the fraction bigger.
2) Making a denominator smaller makes the fraction bigger.

So, from rule number 1, we can see that (600+x)/800 is GREATER THAN (590+x)/800
In other words, (600+x)/800 > (590+x)/800

From rule number 2, we can see that (600+x)/790 is GREATER THAN (600+x)/800
In other words, (600+x)/790 > (600+x)/800

Combine the inequalities to get: (600+x)/790 > (600+x)/800 > (590+x)/800
So, we can be certain that (600+x)/790 > (590+x)/800

Show: ::
B


Cheers,
Brent
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Re: GRE Math Challenge #104 [#permalink] New post   17 Aug 2019, 16:49
GreenlightTestPrep wrote:
sandy wrote:
x > 0

Quantity A: (590+x)/800
Quantity B: (600+x)/790


Two nice rules concerning fractions with positive numerators and denominators:
1) Making a numerator bigger makes the fraction bigger.
2) Making a denominator smaller makes the fraction bigger.

So, from rule number 1, we can see that (600+x)/800 is GREATER THAN (590+x)/800
In other words, (600+x)/800 > (590+x)/800

From rule number 2, we can see that (600+x)/790 is GREATER THAN (600+x)/800
In other words, (600+x)/790 > (600+x)/800

Combine the inequalities to get: (600+x)/790 > (600+x)/800 > (590+x)/800
So, we can be certain that (600+x)/790 > (590+x)/800

Show: ::
B


Cheers,
Brent


Hi Brent,

I got the correct answer independently but I think it was just dumb luck. Can you please help steer me in the right direction if there are flaws in my logic? I simplified both QA and QB by dividing both by 10 to get QA: (59+x)/80 and QB: (60+x)/79. Then I decided that the overall impact of x was unimportant because it would be the same on both sides so I gave x a value of 1 for both quantities. I was left to compare QA: 60/80 and QB: 61/79. I decided that QB was greater because the denominator was smaller and the differences in the numerator was too minuscule to matter.
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Re: GRE Math Challenge #104- x > 0 [#permalink] New post   19 Jun 2021, 06:39
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We need to compare (590+x)800 and (600+x)790
and we know that x > 0

Now, lets look at the numerator of both the quantities

Numerator for Quantity A (590+x) < Numerator for Quantity B (600+x)

Now, lets look at the denominator of both the quantities

Denominator for Quantity A (800) > Denominator for Quantity B (790)

Since Numerator of Quantity A < Numerator of Quantity B and Denominator for Quantity A > Denominator for Quantity B
[numerical example 12/20 < 13/19]

So, Quantity A < Quantity B

So, Answer will be B
Hope it helps!
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GRE Math Challenge #104- x > 0 [#permalink] New post   19 Jun 2021, 06:43
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JNeen

Just adding few things in your solution
When you are dividing both numerator and denominator by 10 then even x will become x10

Now, x/10 can be assumed as X, lets continue with the solution and we know that X will also be > 0

Now, We know that 59/80 < 60/79 so Quantity A < Quantity B
So we can ignore X/80 and X/79 as in any case X/80 < X/79 and it will add to Quantity A < Quantity B
So, your approach was more or less correct with these minor additions.
Good work!
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Re: GRE Math Challenge #104- x > 0 [#permalink] New post   26 Aug 2022, 20:41
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Re: GRE Math Challenge #104- x > 0 [#permalink]
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