If m/n

Question

GMATBusters’ Quant Quiz Question -7

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If m/n < 0 and n - m < 0, which of the following must be true?

i) m > 0
ii) n > 0
iii) 1/m > 1/n

A) i only
B) ii only
C) i & iii only
D) ii & iii only
E) i, ii, iii

Show Answer

Official Answer

C

GMATBusters · Answer

Official Solution:

If m/n<0 and n-m < 0, which of the following must be true?
i) m > 0
ii) n > 0
iii) 1/m > 1/n

m/n<0 means m & n are of opposite sign.
one is positive other is negative
nd n-m < 0 means m>n
So, m must be +ve so,
statement 1 must be true.

n<0
Statement 2 is wrong

if m>n

we can take reciprocal both sides without flipping the inequality sign when both sides are of opposite sign.
we can take reciprocal both sides with flipping the inequality sign when both sides are of the same sign.
if we don't know about the signs, we cannot take reciprocal.

Since, both are of opposite sign, 1/m > 1/n

iii) is true.
Hence, i & iii only are true.

A) i only
B) ii only
C) i & iii only
D) ii & iii only
E) i, ii, iii

Answer C

Raxit85 · Answer

If m/n<0 and n-m < 0, which of the following must be true?
i) m > 0
ii) n > 0
iii) 1/m > 1/n

m/n<0 means either one is negative and n-m < 0 means m>n
So, m must be +ve so, statement 1 must be true.
Statement 2 is wrong as it must be -ve.
1/m > 1/n
if m = 2 and n = -2
1/2 > -1/2, yes
if m = 1/5 and n =-2
5>-1/2, yes

A) i only
B) ii only
C) i & iii only
D) ii & iii only
E) i, ii, iii

Ans. C

sarphant123 · Answer

If m/n<0 and n-m < 0, which of the following must be true?
i) m > 0
ii) n > 0
iii) 1/m > 1/n

m/n<0 means either one is negative and n-m < 0 means m>n
So, m must be +ve so, statement 1 must be true.
Statement 2 is wrong as it must be -ve.
1/m > 1/n
if m = 2 and n = -2
1/2 > -1/2, yes
if m = 1/5 and n =-2
5>-1/2, yes

A) i only
B) ii only
C) i & iii only
D) ii & iii only
E) i, ii, iii

Ans. C

ashwini2k6jha · Answer

m/n=+/-<0 as given m>n ie m+ve ,n-ve
hence m>0,correct
and 1/m>1/n correct
Answer C

Archit3110 · Answer

given
m/n<0 and n-m<0
possible when
n>m and m is +ve and n is -ve
out of given options 1 & 3 are correct

check with m=1 and n = -2 and m = 1/2 and n = -3/2

OPTION C

If m/n<0 and n-m < 0, which of the following must be true?
i) m > 0
ii) n > 0
iii) 1/m > 1/n

A) i only
B) ii only
C) i & iii only
D) ii & iii only
E) i, ii, iii

Hupadhayay · Answer

1. n-m<0 => n one of m or n has to be -ve => from 1. n is -ve and m is +ve Statements: i) m > 0 --> true ii) n > 0 --> false iii) 1/m > 1/n --> taking reciprocals-- -ve number will still be smaller. ------ ex- -4 < 2==> -1/4 < 1/2 ------- so 3rd is true. as we already established m is +ve and n is -ve. Answer: C) i & iii only

uc26 · Answer

m/n<0 means that m and n have opposite signs. n-m<0 means n0 and iii) 1/m> 1/n must be true. Answer: C

Kinshook · Answer

Asked: If m/n<0 and n-m < 0, which of the following must be true?

m/n<0; m & n have opposite signs; (m>0 & n<0) or (m<0 & n>0)
n-m<0; n<m; m>0 & n<0

i) m > 0
MUST BE TRUE
ii) n > 0
MUST BE FALSE
iii) 1/m > 1/n
Since m>0;1/m>0 & n<0;1/n<0
1/m>0>1/n
MUST BE TRUE

IMO C

Abhishek009 · Answer

Plug in and check m = 1 & n = -2 \frac{m}{n}<0 = -\frac{1}{2} < 0 & n-m < 0 = -3 < 0 Now, Check the options - i) m > 0 ( True) 1 > 0 ii) n > 0 (False) -2 < 0 iii) \frac{1}{m} > \frac{1}{n} ( True) 1 > -\frac{1}{2} Hence, Answer must be (C)

Jawad001 · Answer

If m/n<0 and n-m < 0, which of the following must be true?
i) m > 0
ii) n > 0
iii) 1/m > 1/n

A) i only
B) ii only
C) i & iii only
D) ii & iii only
E) i, ii, iii

Solution:

Given:
m/n<0 and n-m < 0
From m/n< 0, either m or n is negative.
From n – m < 0,
n < m

From above both statements, it can be said that m > 0.
Answer: A

StevenA · Answer

If m/n<0 and n-m < 0, which of the following must be true?
i) m > 0
ii) n > 0
iii) 1/m > 1/n

m/n<0 means either one is negative and n-m < 0 means m>n
So, m must be +ve so, statement 1 must be true.
Statement 2 is wrong as it must be -ve.
1/m > 1/n
if m = 2 and n = -2
1/2 > -1/2, yes
if m = 1/5 and n =-2
5>-1/2, yes

A) i only
B) ii only
C) i & iii only
D) ii & iii only
E) i, ii, iii

Ans. C

freedom128 · Answer

01) m/n < 0
This means that m and n must have different sign, ie. m is +ve and n is -ve, and vice versa. Neither m nor n is zero.

02) n - m < 0 --> n < m
Because m and n must have different signs, it is logical that m is +ve and n is - ve.

Let's review one by one

i) m > 0
MUST BE TRUE. This is aligned with the explanation in 02)

ii) n > 0
FALSE. This contradicts with the explanation in 02)

iii) 1/m > 1/n
Because m is +ve and n is -ve, this MUST BE TRUE.

FINAL ANSWER IS (C) i & iii only

Posted from my mobile device

NunuBot · Answer

Given that:
m / n < 0 ---(1)
n - m < 0 --- (2)

From (2):
n < m ---(3)

From (1) and (3):
m must be positive (i.e. m > 0) >> (i) is True
n must be negative (i.e. n < 0) >> (ii) is False

Since:
n < m --- (3) and
m is Positive
n is Negative

Then:
(divide by mn on both sides, flip sign once)
1/m > 1/n >> (iii) is True

Alternatively note that:
m is Positive >> 1/m is Positive
n is Negative >> 1/n is Negative
Therefore: 1/m > 1/n >> (iii) is True

Answer: (i) and (iii) must be true, C

suchita2409 · Answer

IMO C

1) m and n has opposite signs for sure .
2) m is greater than n 
(from Q.S.)

therefore
m has to be + ve
n has to be - ve

1 stmt is correct
m is greater than n
2 stmt is incorrect
3 stmt is correct since even the reciprocal of -ve is less than the reciprocal of positive

Posted from my mobile device

shameekv1989 · Answer

m/n < 0 => i)m=+ve and n=-ve or ii) m=-ve and n=+ve Since n Case ii) is invalid. Hence m > 0 and n < 0 i) m > 0 must always be true ii) n > 0 will never be true iii) Since n 1/n > 1/m - Not true Only i) must be true Answer - A

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If m/n < 0 and n - m < 0, which of the following must be true?

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