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

Question

Find the maximum value of a*b? 1) a and b are prime numbers 2) a+b = 10 Source: www.GMATinsight.com

PKN · Answer

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)

sachinkumardalal1303 · Answer

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

Posted from my mobile device

sachinkumardalal1303 · Answer

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

Posted from my mobile device

Kaczet · Answer

a+b=10
a*b-> max

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

a*b=25

oblivion441 · Answer

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

ParthSanghavi · Answer

Bunuel   VeritasKarishma

Please Help

rishab0507 · Answer

Statement 1 is clearly insufficient

Statement 2 : Not necessarily we need to look for prime, Given a+b =10, a multiple of a number is greater of its sums digits when both digits are same. This is a theory, You can try with any number. thus sum of 10 will be greater with digits 5+5 =10, 5*5= 25

moana123 · Answer

Find the maximum value of a*b?

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

----------

Question for #2 (echoing one of the previous posts).

2) a + b = 10

a and b could be:
- 9 and 1
- 8 and 2
- 7 and 3
- 6 and 4
- 5 and 5

I understand that 5 and 5 would yield the max a*b but is ok to assume these two numbers ARE A&B in GMAT when there are 4 other pairs possible based on statement #2? Pls help

----

Bunuel VeritasKarishma

---- Bunuel VeritasKarishma

KarishmaB · Answer

Since we are looking for the maximum value of a*b, we do need to pin point to the values of a and b which yield us the max value of a*b. Since 5 and 5 do that, it works. Though I am never happy with DS questions asking for max/min values. When do you have enough information? As you keep adding constraints, max/min values keep changing.

srik410 · Answer

For any two numbers, AM>=GM. So a+b/2>=sqrt(ab). 
That gives B

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards