If both m and n are negative integers, which of the following must be

Question

If both m and n are negative integers, which of the following must be positive?

A.  \frac{m}{n}-1

B.  m(n+1)

C.  mn-5

D.  m^2+n^2-1

E.  mn+3n

Sriharsh · Answer

Ans-D

For m,n negative intergers, largest value is -1. Hence option D will be definitely positive all others may be positive negative or 0.

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NandishSS · Answer

We can test all options

Except D all others option will give us negative

Lets take m=n=-1

m^2+n^2-1  = 1 Which is positive

Hence D

Archit3110 · Answer

Out of the given options , D seems to suit well the situation as for the rest we will get either + , 0 or -ve values....

Salsanousi · Answer

Let m and n be -1

For A) -1/-1 - 1 = 1-1 = 0 not positive

For B) -1 (-1+1) = -1 * 0 = 0 not positive

For C) 1 - 5 = -4 not positive

For D) (-1)^2 + (-1)^2 - 1 = 1 + 1 - 1 = 2 - 1 = 1 is positive

For E) (-1)*(-1) + 3 (-1) = 1 - 3 = -2

Answer choice D

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Archit3110 · Answer

Hello  Salsanousi  , by your comment of '0 not positive ' , you mean to say that '0' is not a + ve integer? in GMAT is a 0 + even integer , negating options with 0 is not correct way , you can check with values as -m>-n and vice versa you would get both + & - ve answers which is why the option would be wrong...

Salsanousi · Answer

Hi Archit3110 in GMAT when we say an integer is positive we mean it is > 0

0 is neither positive nor negative.

For more on that please check this https://gmatclub.com/forum/math-number- ... 88376.html

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EgmatQuantExpert · Answer

Solution 
  Given:  
 • Both m and n are negative integers

To find:  
 • Which of the given answer choices is positive?

Approach and Working:   
 • Option A:  (\frac{m}{n}) – 1 
 o If m < n, then it is positive, else it is not positive

• Option B: m(n + 1)
 o If n > -1 then it is positive, else it is not positive

• Option C: mn - 5
 o If mn > 5 then it is positive, else it is not positive

• Option D:  m^2 + n^2 - 1 
 o Minimum value of  m^2 + n^2 = 1 + 1 = 2 
o Thus, minimum value of  m^2 + n^2 – 1 = 1 
o Therefore, it is always positive

• Option E: mn + 3n = n(m + 3)
 o If m > -3 then it is positive, else it is not positive

Hence, the correct answer is Option D

Answer: D

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-NP-e1533292144892.png

Bunuel · Answer

ZERO.

1. 0 is an integer.

2. 0 is an even integer. An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Archit3110 · Answer

Bunuel  thanks for sharing i understand that 0 is not +ve or -ve integer... but I have a doubt for a consecutive series of even integers would we start count from (0,2,4,6 ...) or (2,4,6,8...)

Bunuel · Answer

If a question says for example "a set of three consecutive even integers ...", then the set cannot have 0 or any negative even integer in it. The smallest set in this case can be {2, 4, 6}.

kapstone1996 · Answer

Given that N & M are integers, the largest negative number is -1. I used this to test each given answer. Only answer choice D fits.

If both m and n are negative integers, which of the following must be

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GMAT Problem Solving (PS) Questions

If both m and n are negative integers, which of the following must be

Prep Toolkit

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