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GRE Math Challenge #66- Square Root of 2
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Updated on: 19 Feb 2020, 11:48
Updated on: 19 Feb 2020, 11:48
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13% (00:25) wrong based on 92 sessions
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Quantity A |
Quantity B |
\((1 + \sqrt{2})^2\) |
3 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #66- Square Root of 2
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24 Sep 2017, 14:57
24 Sep 2017, 14:57
2
sandy wrote:
Quantity A: \((1 + \sqrt{2})^2\)
Quantity B: 3
Quantity B: 3
There are a few ways to handle this question.
One is to use some approximation.
On test day, it's a good idea to know the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
So, we get something like this:
Quantity A: (1 + 1.4)²
Quantity B: 3
Simplify:
Quantity A: (2.4)²
Quantity B: 3
ASIDE: if √5 ≈ 2.2, then we know that (2.2)² ≈ 5
So, (2.4)² = a number that's bigger than 5
So, we have:
Quantity A: a number that's bigger than 5
Quantity B: 3
Answer: A
Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #66- Square Root of 2
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24 Sep 2017, 15:01
24 Sep 2017, 15:01
1
sandy wrote:
Quantity A: \((1 + \sqrt{2})^2\)
Quantity B: 3
Quantity B: 3
Another approach is to use the FOIL method and matching operations
Given:
Quantity A: (1 + √2)²
Quantity B: 3
Use the FOIL method to expand Quantity A:
Quantity A: 1 + √2 + √2 + 2
Quantity B: 3
Simplify:
Quantity A: 3 + 2√2
Quantity B: 3
Subtract 3 from both sides:
Quantity A: 2√2
Quantity B: 0
Quantity A is clearly bigger than Quantity B
Answer: A
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