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04 May 2022, 03:30
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Difficulty:
5%
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Question Stats:
90% (00:53) correct
10%
(00:48)
wrong
based on 72
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If a and b are positive integers, what is the value of ab?
(1) ab is divisible by 6.
(2) a and b are prime numbers.
(1) ab is divisible by 6.
(2) a and b are prime numbers.
09 May 2022, 09:16
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Statement 1:
ab is divisible by 6 means value of ab is any multiple of 6. Endless values we can find
So, Statement 1 is not sufficient alone
Statement 2:
a and b are just prime numbers. The values can be anything like (3*2), (5*7), .......
So, statement 2 is not sufficient alone
Now lets analyse it together
Since ab is divisible by 6 so the value can be
6*1=6
6*2=12
6*3=18
6*4=24
6*5=30
6*6=36
Lets leave it here
Now since a and b are prime numbers so we have to check how to get to 1,2,3,4,5,6....
1=1*1 (a=1, b=1) not prime
2=2*1 not prime
Lets test for 4
4=2*2 (a=2,b=2) both a and b are primes, so ab=2*2=4
Lets test for 6
6=3*2 (a=3,b=2) both a an b are primes, so ab=6
So, both statements together is also not giving a certain answer.
Answer choice E
ab is divisible by 6 means value of ab is any multiple of 6. Endless values we can find
So, Statement 1 is not sufficient alone
Statement 2:
a and b are just prime numbers. The values can be anything like (3*2), (5*7), .......
So, statement 2 is not sufficient alone
Now lets analyse it together
Since ab is divisible by 6 so the value can be
6*1=6
6*2=12
6*3=18
6*4=24
6*5=30
6*6=36
Lets leave it here
Now since a and b are prime numbers so we have to check how to get to 1,2,3,4,5,6....
1=1*1 (a=1, b=1) not prime
2=2*1 not prime
Lets test for 4
4=2*2 (a=2,b=2) both a and b are primes, so ab=2*2=4
Lets test for 6
6=3*2 (a=3,b=2) both a an b are primes, so ab=6
So, both statements together is also not giving a certain answer.
Answer choice E
29 May 2022, 15:34
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AritraKundu
Statement 1:
ab is divisible by 6 means value of ab is any multiple of 6. Endless values we can find
So, Statement 1 is not sufficient alone
Statement 2:
a and b are just prime numbers. The values can be anything like (3*2), (5*7), .......
So, statement 2 is not sufficient alone
Now lets analyse it together
Since ab is divisible by 6 so the value can be
6*1=6
6*2=12
6*3=18
6*4=24
6*5=30
6*6=36
Lets leave it here
Now since a and b are prime numbers so we have to check how to get to 1,2,3,4,5,6....
1=1*1 (a=1, b=1) not prime
2=2*1 not prime
Lets test for 4
4=2*2 (a=2,b=2) both a and b are primes, so ab=2*2=4
Lets test for 6
6=3*2 (a=3,b=2) both a an b are primes, so ab=6
So, both statements together is also not giving a certain answer.
Answer choice E
ab is divisible by 6 means value of ab is any multiple of 6. Endless values we can find
So, Statement 1 is not sufficient alone
Statement 2:
a and b are just prime numbers. The values can be anything like (3*2), (5*7), .......
So, statement 2 is not sufficient alone
Now lets analyse it together
Since ab is divisible by 6 so the value can be
6*1=6
6*2=12
6*3=18
6*4=24
6*5=30
6*6=36
Lets leave it here
Now since a and b are prime numbers so we have to check how to get to 1,2,3,4,5,6....
1=1*1 (a=1, b=1) not prime
2=2*1 not prime
Lets test for 4
4=2*2 (a=2,b=2) both a and b are primes, so ab=2*2=4
Lets test for 6
6=3*2 (a=3,b=2) both a an b are primes, so ab=6
So, both statements together is also not giving a certain answer.
Answer choice E
Hey there, this is incorrect.
Your logic for ruling out A,B, and D are all correct. Which means the answer is either C or E.
The answer is C, this is because we know that a*b are BOTH prime and we know that the product a*b is ALSO a multiple of 6. In other words, a*b is EVEN
In order for this to be true, one of the prime numbers HAS to be 2. Because all prime numbers but 2 are odd, then odd*odd = odd. Which means if NEITHER 'a' NOR 'b' are 2, then a*b HAS to be odd, and this goes against statement 1. This tells us that either a or b is 2. So let's say that a=2, then we know from statement 1 that ab has to be a multiple of 6 whilst 'b' is also prime... is this possible? Yes, it is possible, this is only possible if b=3 when a=2. Hence, a and b are BOTH prime and a*b is a multiple of 6 and this is the only case that will work. So C is the answer.
