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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, 05:16
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Difficulty:

  45% (medium)

Question Stats:

53% (01:08) correct 47% (00:57) wrong based on 147 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, 05:42
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, 05:49
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, 05:50
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, 08:36
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 =  [#permalink]

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New post 03 Dec 2018, 04:55
1
PKN wrote:
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)



Hi there!

Sorry but in statement number 2 you say "Since prime numbers.." But unless you use statement A, you cannot tell if a and b are prime numbers. They could be any number: 7+3 / 8+2 / 9+1

Can you kindly explain to me how you came up with the fact that they are both prime numbers?

Also another question (more general): aren't a and b supposed to be DIFFERENT numbers since they are defined with different variables?

Thank you very very much :)
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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 03 Dec 2018, 10:12
oblivion441 wrote:
PKN wrote:
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)



Hi there!

Sorry but in statement number 2 you say "Since prime numbers.." But unless you use statement A, you cannot tell if a and b are prime numbers. They could be any number: 7+3 / 8+2 / 9+1

Can you kindly explain to me how you came up with the fact that they are both prime numbers?

Also another question (more general): aren't a and b supposed to be DIFFERENT numbers since they are defined with different variables?

Thank you very very much :)


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Re: Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b =   [#permalink] 03 Dec 2018, 10:12
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