If a and b are non zero integers is ab/(a + b)

Question

If a and b are non zero integers is ab/(a + b) < ab?

(1) a = 6b
(2) a + b < 0

kntombat · Answer

Bunuel ,  yashikaaggarwal  can either of you help as and when possible?

Thank you.

yashikaaggarwal · Answer

kntombat

(1) a = 6b
From above, we know a and b has the same signs (both positive, both negative)
Case 1: a = 6, & b = 1
ab/(a + b) < ab
6/7 < 6 (true)

Case 2: a = -6, & b = -1
ab/(a + b) < ab
6/-7 < 6 (true)
(Sufficient)

(2) a + b < 0
a and b can both negative or one negative and one positive (but negative value is greater than positive value)

Case 1: a = -6, & b = -1
ab/(a + b) < ab
6/-7 < 6 (true)

Case 2: a = -6, & b = 1
ab/(a + b) < ab
-6/5 > -6 (false)
(Insufficient)

Answer is A

Posted from my mobile device

Kinshook · Answer

Asked: If a and b are non zero integers is ab/(a + b) < ab?
Is ab/(a+b) < ab?
Is ab/(a+b) - ab < 0?
Is ab {1/(a+b) - 1} < 0?
Is 1/(a+b) - 1 < 0?
Is 1/(a+b) < 1?
Is (a+b) > 1?

(1) a = 6b
If b is -ve ; a is -ve and ab<0
But if b = 2; a=12; ab=24 > 1
NOT SUFFICIENT

(2) a + b < 0
a + b < 0
a + b is NOT >1
SUFFICIENT

IMO B

AndrewN · Answer

I took a simple approach to this one that led to a clear and fast answer.

Statement (1)

Substitute for  a :

\frac{6b*b}{6b + b} < 6b*b

\frac{6b^2}{7b} < 6b^2

Now, we can plainly see that  both sides contain 6b squared, and we know that since  b  must be a nonzero integer, this product must be positive . We can thus reimagine the inequality:

\frac{POS}{7b} < POS

Now,  if  b  is positive, the right-hand side must be greater , since we would be taking the same value on the left-hand side and dividing by a multiple of 7.  If, on the other hand,  b  is negative, the left-hand side will be negative, while the right-hand side will remain positive.  Thus, regardless of whether  b  is positive or negative, the answer to the question is YES, and   Statement (1) is SUFFICIENT  .

Statement (2)

Substitute for (a + b), keeping things as simple as possible:

\frac{ab}{NEG} < ab

Now, we know nothing about  a  and  b  individually, so we can think of their product (as  nonzero integers , remember) as either positive or negative.

a)  ab  is positive—

\frac{POS}{NEG} < POS   True .

b)  ab  is negative—

\frac{NEG}{NEG} < NEG   False .

Since we get conflicting results, we can   rule out Statement (2) as sufficient on its own  .

The answer must be (A).

Good luck with your studies, everyone.

- Andrew

saurabhbajpai · Answer

Even I followed the same approach. But OA doesn't match.

Posted from my mobile device

saurabhbajpai · Answer

This matches my solution but OA is dufferent

Posted from my mobile device

If a and b are non zero integers is ab/(a + b) < ab?

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If a and b are non zero integers is ab/(a + b) < ab?

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