If product of integers a and b is negative and sum of their squares is

Question

If product of integers a and b is negative and sum of their squares is greater than 0 but less than 86, then what is the maximum value of ab?

A. -42
B. -36
C. -18
D. -9
E. -1

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LeoN88 · Accepted Answer

If product of integers a and b is negative and sum of their squares is greater than 0 but less than 86, then what is the maximum value of ab?

Hey what if I consider two integers 1 & -1.
0<1^2 + (-1)^2<86
ab= -1

-1 is greater than -9, hence maximum value.

chaitanya2402 · Answer

a x b < 0 i.e either a or b is -ve.

0<a^2 + b^2<86

The square neartest to 86 is 81 (9^2).

If one of the variable is 9 then other one must be smallest and 1.

Possible combinations are 9,-1 or -9,1 eitherway their product is -9.

IMO D.

AkshdeepS · Answer

If a = -9 and b = 1 ----- a^2 + b^2 = 81+1 = 82

ab = -9*1 = -9

If a = -9 and b = 2 ------ a^2 + b^2 = 81+4 = 85

ab = -9*2 = -18

If a = -7 and b = 6 ------ a^2 + b^2 = 49 + 36 = 85

ab = -7*6 = -42

Finding it difficult to understand what the question is exactly asking?

If it is asking in terms of absolute value then correct answer will be -42.

In general terms, possible maximum value should be -9.

Let us wait for the OA.

medic19 · Answer

A IMO - Work Backwards and sign matter little here when testing everything since we square each a and b - Start from max numbers for -36 = 6*-6; 36+36=72; Try max numbers for 42 = 7*-6; 49+36 = 85, just about fits

AkshdeepS · Answer

Yes, possible. I thought along the same line, but still wary of the language as it confuses me.

Manat · Answer

We need to find the maximum value of AB and not A & B individually or the maximum sum of their squares,

-1 can be written as 1 X -1,

(1)^2 + (-1)^2 =0

Satisfies both the conditions and is the maximum value.

Archit3110 · Answer

given 
a*b=-ve ; so either of a or b is -ve integer and
0<a^2+b^2<86

use answer options to solve
  A.  -42 ; -2*21 ; not possible to big value of a^2+b^2
 B.  -36 ; can be -2*18,-4*9,-6*6 ; again a^2+b^2 is to big
 C.  -18; can be -2*9; -3*6 or 1*-18,; a^2+b^2 large value >86
 D.  -9 ; can be -1*9; -3*3 ; yes seems a good contender
 E.  -1; -1*1 ; yes best of the lot ; lowest value and a^2+b^2 = 2 sufficient

IMO E ; -1

SPatel1992 · Answer

Hi! Really nice approach. That's what I started out with, but then I thought if we included fractions:
e.g.
a= 1/4 and b= -4
Then ab= -1 and 0<a^2 +b^2< 86 
(1/16) +16 would still be less than 86

shhivaa · Answer

It is C, -18, Product of -9 and 2, Hit and trail.

EgmatQuantExpert · Answer

Solution 
  Given:  
In this question, we are given
 • The product of integers a and b is negative
• The sum of the squares of a and b is greater than 0 but less than 86

To find:  
We need to determine
 • The maximum value of ab

Approach and Working:  
As the product of ab is negative, one of a and b must be negative and both of them are non-zero.
 • Hence, to maximise the value of ab, we must consider the minimum possible value for the positive integer (i.e. +1) and the maximum possible value of the negative integer (i.e. -1).
• Therefore, the maximum possible value of ab = (1) x (-1) = -1

Hence, the correct answer is option E.

Answer: E

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If product of integers a and b is negative and sum of their squares is

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If product of integers a and b is negative and sum of their squares is

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