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If product of integers a and b is negative and sum of their squares is
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15 May 2019, 02:07
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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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Re: If product of integers a and b is negative and sum of their squares is
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15 May 2019, 02:13
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.



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Re: If product of integers a and b is negative and sum of their squares is
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15 May 2019, 02:19
Hi why not 7 & 6 Sum of the squares is 49 + 36 = 85 which is less than 86 Product is 42
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Re: If product of integers a and b is negative and sum of their squares is
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15 May 2019, 03:59
EgmatQuantExpert wrote: 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 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.
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Re: If product of integers a and b is negative and sum of their squares is
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15 May 2019, 04:13
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



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Re: If product of integers a and b is negative and sum of their squares is
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15 May 2019, 04:31
chaitanya2402 wrote: 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. 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.
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Re: If product of integers a and b is negative and sum of their squares is
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15 May 2019, 04:37
LeoN88 wrote: chaitanya2402 wrote: 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. 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. Yes, possible. I thought along the same line, but still wary of the language as it confuses me.
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Re: If product of integers a and b is negative and sum of their squares is
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15 May 2019, 08:05
EgmatQuantExpert wrote: 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 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.



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Re: If product of integers a and b is negative and sum of their squares is
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15 May 2019, 08:21
LeoN88 wrote: chaitanya2402 wrote: 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. 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. Posted from my mobile device



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If product of integers a and b is negative and sum of their squares is
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15 May 2019, 10:51
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 EgmatQuantExpert wrote: 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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Re: If product of integers a and b is negative and sum of their squares is
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16 May 2019, 10:46
chaitanya2402 wrote: 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. 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



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Re: If product of integers a and b is negative and sum of their squares is
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17 May 2019, 23:01
It is C, 18, Product of 9 and 2, Hit and trail.



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Re: If product of integers a and b is negative and sum of their squares is
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18 May 2019, 02:26
Please can you clarify the difference between Value and Number? Does the question not ask for the 'value' (rather than 'number') and the sign should therefore be ignored?



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If product of integers a and b is negative and sum of their squares is
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Updated on: 20 May 2019, 10:29
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 nonzero. • 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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Re: If product of integers a and b is negative and sum of their squares is
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20 May 2019, 08:45
EgmatQuantExpertplease see highlighted part , typo error.. EgmatQuantExpert wrote: 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 nonzero. • 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: B



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Re: If product of integers a and b is negative and sum of their squares is
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20 May 2019, 10:29
Archit3110 wrote: EgmatQuantExpertplease see highlighted part , typo error.. Rectified...Thanks
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Re: If product of integers a and b is negative and sum of their squares is
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