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sqrt135/sqrt15
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04 Nov 2020, 11:23
04 Nov 2020, 11:23
Expert Reply
00:00
Question Stats:
68% (00:41) correct
31% (00:55) wrong based on 63 sessions
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Quantity A |
Quantity B |
\(\frac{\sqrt{135}}{\sqrt{15}}\) |
\(\frac{\sqrt{117}}{\sqrt{13}}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Source: 320 GRE Math Questions
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: sqrt135/sqrt15
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13 Nov 2020, 17:36
13 Nov 2020, 17:36
1
Carcass wrote:
Quantity A |
Quantity B |
\(\frac{\sqrt{135}}{\sqrt{15}}\) |
\(\frac{\sqrt{117}}{\sqrt{13}}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Source: 320 GRE Math Questions
Useful property: \(\frac{\sqrt{x}}{\sqrt{y}}=\sqrt{\frac{x}{y}}\)
We get:
QUANTITY A: \(\frac{\sqrt{135}}{\sqrt{15}}=\sqrt{\frac{135}{15}}=\sqrt{9}\)
QUANTITY B: \(\frac{\sqrt{117}}{\sqrt{13}}=\sqrt{\frac{117}{13}}=\sqrt{9}\)
Answer: C
Re: sqrt135/sqrt15
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20 Nov 2020, 13:46
20 Nov 2020, 13:46
A little surprised at the percentages(40-60 at the time of writing). I think there is one thing we can know considering it is tagged as hard, but first things first: since it has no variables, we can eliminate D. On the test, we might not know what is hard, but we have an idea that as we get later into the math section, the difficulty increases. Therefore, we might suspect some trick. So even if we just used the calculator, we might be able to suspect when they are very close that C is a really good possibility. I give this long preface because I am making an assumption that anyone who could see, mostly likely in A, that the numerator's 135 has as a factor 15 and therefore can be re-written by making 9*15 under the radical, simplifying to 3 root 15 and then reduced just plain 3, got it right. The same can be done for the other one.
