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GRE Math Challenge #104- x > 0
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09 May 2015, 11:22
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 is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
Quantity A |
Quantity B |
\(\frac{(590+x)}{800}\) |
\(\frac{(600+x)}{790}\) |
• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #104
[#permalink]
12 May 2015, 08:30
12 May 2015, 08:30
sandy wrote:
x > 0
Quantity A: (590+x)/800
Quantity B: (600+x)/790
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
Re: GRE Math Challenge #104
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17 Aug 2019, 16:49
17 Aug 2019, 16:49
GreenlightTestPrep wrote:
sandy wrote:
x > 0
Quantity A: (590+x)/800
Quantity B: (600+x)/790
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.
