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(3+5)(3+5) or 20
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25 Jun 2021, 05:05
25 Jun 2021, 05:05
Expert Reply
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Question Stats:
100% (00:37) correct
0% (00:00) wrong based on 13 sessions
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Quantity A |
Quantity B |
\([3+\sqrt{5}][3+\sqrt{5}]\) |
20 |
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.
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Location: India
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Re: (3+5)(3+5) or 20
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25 Jun 2021, 05:35
25 Jun 2021, 05:35
1
Carcass wrote:
Quantity A |
Quantity B |
\([3+\sqrt{5}][3+\sqrt{5}]\) |
20 |
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.
Col. A: \((3 + \sqrt{5})^2\)
Col. B: \(20\)
Col. A: \((3)^2 + (\sqrt{5})^2 + 2(3)(\sqrt{5})\)
Col. B: \(20\)
Col. A: \(14 + 6\sqrt{5}\)
Col. B: \(20\)
Subtracting \(14\) from both sides;
Col. A: \(6\sqrt{5}\)
Col. B: \(6\)
Dividing by \(6\) both sides;
Col. A: \(\sqrt{5}\)
Col. B: \(1\)
Hence, option A
Another Approach:
Plug in the value of \(\sqrt{5} = 2.23\)
Col. A: \((3 + \sqrt{5})^2\)
Col. B: \(20\)
Col. A: \((3 + 2.23)^2\)
Col. B: \(20\)
Col. A: \(5.23^2\)
Col. B: \(20\)
Col. A: \(27.35\)
Col. B: \(20\)
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(3+5)(3+5) or 20
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26 Jun 2021, 05:11
26 Jun 2021, 05:11
Carcass wrote:
Quantity A |
Quantity B |
\([3+\sqrt{5}][3+\sqrt{5}]\) |
20 |
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.
3 useful approximations to have memorized for test day:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
So, we get:
QUANTITY A: \([3+\sqrt{5}][3+\sqrt{5}]≈(3+2.2)(3+2.2)≈(5.2)(5.2)\)
QUANTITY B: \(20\)
Since (5)(5) = 25, we know that (5.2)(5.2) is greater than 25, which means (5.2)(5.2) is greater than 20
Answer: A
