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Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =

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Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =  [#permalink]

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New post 16 Aug 2018, 04:16
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A
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Difficulty:

  55% (hard)

Question Stats:

45% (00:48) correct 55% (00:50) wrong based on 75 sessions

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Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =  [#permalink]

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New post 16 Aug 2018, 04:42
GMATinsight wrote:
Find the maximum value of a*b?

1) a and b are prime numbers
2) a+b = 10

Source: http://www.GMATinsight.com


Question stem:- Max(a*b)=?

St1:- a and b are prime numbers.

There are infinite numbers of prime numbers in number system.
So, the value of the product of two prime numbers is not unique.
Insufficient.

St2:- a+b = 10
Since prime numbers, by definition are positive in nature.
And the product a*b is maximum when a and b are maximum satisfying the given condition.
So, a=b=5 yields the max(a*b).
we got an unique value of a*b, hence sufficient.

Ans. (B)
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =  [#permalink]

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New post 16 Aug 2018, 04:49
To find. Maximum value of a*b
1) in first v r given a and b r prime numbers
But there r infinite prime numbers so v can't find out maximum value of a*b
So 1) is insufficient
Means answers would be among b,c,and e

2) v r given a+b =10. From which v can use hint and trial method and get that 5*5 can give us maximum value of a*b

So 2) is sufficient and our answer is b

ANSWER b

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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =  [#permalink]

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New post 16 Aug 2018, 04:50
To find. Maximum value of a*b
1) in first v r given a and b r prime numbers
But there r infinite prime numbers so v can't find out maximum value of a*b
So 1) is insufficient
Means answers would be among b,c,and e

2) v r given a+b =10. From which v can use hint and trial method and get that 5*5 can give us maximum value of a*b

So 2) is sufficient and our answer is b

ANSWER b

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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =  [#permalink]

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New post 16 Sep 2018, 07:36
a+b=10
a*b-> max

ab=a(10-a)
f'(x)=10-2a => a=5; b=10-a => b=5

a*b=25
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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = &nbs [#permalink] 16 Sep 2018, 07:36
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Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =

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