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Which of the following pairs are not reciprocals of each other? (Mark
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31 Mar 2025, 04:33
31 Mar 2025, 04:33
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Which of the following pairs are not reciprocals of each other? (Mark all the correct answers)
(A) $\(\sqrt{5}-2\)$ and $\((\sqrt{5}-2)^{-1}\)$
(B) $\(7^{-1}$ and $-7^{-1}\)$
(C) 13 and $1\(3^{-1}\)$
(D) $\(\sqrt{3}-\sqrt{2}\)$ and $\(\sqrt{3}+\sqrt{2}\)$
(E) $\(\sqrt{a}\)$ and $\(\frac{\sqrt{a}}{a}\)$
(F) 2 and -2
(G) $\(\sqrt{7}+7\)$ and $\((-\sqrt{7}+7)\)$
(A) $\(\sqrt{5}-2\)$ and $\((\sqrt{5}-2)^{-1}\)$
(B) $\(7^{-1}$ and $-7^{-1}\)$
(C) 13 and $1\(3^{-1}\)$
(D) $\(\sqrt{3}-\sqrt{2}\)$ and $\(\sqrt{3}+\sqrt{2}\)$
(E) $\(\sqrt{a}\)$ and $\(\frac{\sqrt{a}}{a}\)$
(F) 2 and -2
(G) $\(\sqrt{7}+7\)$ and $\((-\sqrt{7}+7)\)$
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Re: Which of the following pairs are not reciprocals of each other? (Mark
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04 Apr 2025, 04:00
04 Apr 2025, 04:00
Expert Reply
OFFICIAL EXPLANATION
As the reciprocal of $A$ is $\(1 / A\)$, the reciprocal of $\(7^{-1}=1 / 7\)$ is 7 .
The reciprocal of 2 is $\(1 / 2\)$ and the reciprocal of $\(\sqrt{7}+7 \Rightarrow \frac{1}{7+\sqrt{7}}=\frac{7-\sqrt{7}}{49-7}=\frac{7-\sqrt{7}}{42}\)$.
Therefore, only $B, F$ and $G$ are not reciprocals to each other.
Thus, the correct answer choices are $B, F$ and $G$.
As the reciprocal of $A$ is $\(1 / A\)$, the reciprocal of $\(7^{-1}=1 / 7\)$ is 7 .
The reciprocal of 2 is $\(1 / 2\)$ and the reciprocal of $\(\sqrt{7}+7 \Rightarrow \frac{1}{7+\sqrt{7}}=\frac{7-\sqrt{7}}{49-7}=\frac{7-\sqrt{7}}{42}\)$.
Therefore, only $B, F$ and $G$ are not reciprocals to each other.
Thus, the correct answer choices are $B, F$ and $G$.
gmatclubot
Re: Which of the following pairs are not reciprocals of each other? (Mark [#permalink]
04 Apr 2025, 04:00
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