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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1879
WE: General Management (Education)
If m/n < 1 which of the following must be greater than 1 ?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 56% (01:31) correct 44% (01:02) wrong based on 36 sessions

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If $$m/n < 1$$ which of the following must be greater than 1 ?

(A) $$\frac{m}{n^2}$$

(B) $$\frac{m}{2n}$$

(C) $$\frac{n}{m^2}$$

(D) $$\frac{n}{m}$$

(E) None of the above

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Re: If m/n < 1 which of the following must be greater than 1 ?  [#permalink]

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GMATBusters wrote:
If $$m/n < 1$$ which of the following must be greater than 1 ?

(A) $$\frac{m}{n^2}$$

(B) $$\frac{m}{2n}$$

(C) $$\frac{m}{n^2}$$

(D) $$\frac{n}{m}$$

(E) None of the above

GMATBusters Collection

Given: $$m/n < 1$$

(A) $$\frac{m}{n^2}$$ If m/n = 1/2, m/n^2 = 1/4 i.e. NOT greater than 1 so ELIMINATED

(B) $$\frac{m}{2n}$$ If m/n = 1/2, m/2n = 1/4 i.e. NOT greater than 1 so ELIMINATED

(C) $$\frac{m}{n^2}$$ If m/n = 1/2, m/n^2 = 1/4 i.e. NOT greater than 1 so ELIMINATED (By mistake it is same option as Option A)

(D) $$\frac{n}{m}$$ If m/n = -1, n/m = -1 i.e. NOT greater than 1 so ELIMINATED

(E) None of the above CORRECT OPTION
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If m/n < 1 which of the following must be greater than 1 ?  [#permalink]

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GMATBusters wrote:
If $$m/n < 1$$ which of the following must be greater than 1 ?

(A) $$\frac{m}{n^2}$$

(B) $$\frac{m}{2n}$$

(C) $$\frac{n}{m^2}$$

(D) $$\frac{n}{m}$$

(E) None of the above

GMATBusters Collection

Remember that we have two possible cases: $$\frac{m}{n}$$ is between 0 and 1, or $$\frac{m}{n}$$ is negative.
If $$\frac{m}{n}$$ is negative then this means m and n have opposite signs. We will check if the answers are forced to be positive first.
(A) m negative n positive, then A is negative.
(B) m negative n positive, then B is negative.
(C) n negative m positive, then C is negative.
(D) n negative m positive, then D is negative.

Therefore in all cases we can't even pass the "must be positive" test, E is the answer.
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# If m/n < 1 which of the following must be greater than 1 ?   