Number System

Question

Hi,
Please provide approach to solve such questions-

Three is the largest number that an be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100
1 – 30
2- 70
3- 210
4 – 300
E – 700

Thanks

sl750 · Answer

We have to pick a number for x that is divisible by both 3 and 10. We have 30, 60, 90, and so on. Therefore the largest integer that divides both x (x=300) and 2100 will be 300

Brent@GMATPrepNow · Answer

imhimanshu wrote:Hi,
Please provide approach to solve such questions-

Three is the largest number that an be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100
1 – 30
2- 70
3- 210
4 – 300
E – 700

Thanks

The fastest approach here might be to use the process of elimination (POE).

E) Can x=700? No - otherwise the greatest common divisor of x and 100 would be 100 (where the question tells us that the GCD of x and 100 is 10)

D) Can x=300? No - otherwise the greatest common divisor of x and 100 would be 100 (where the question tells us that the GCD of x and 100 is 10)

C) Can x=210? Sure, the GCD of 210 and 27 is 3, and the GCD of 210 and 100 is 10
SO, if x=210, then the GCD of x and 2100 will be 210
The answer is C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

knight247 · Answer

SL that is not the right answer.

The largest number that is divisible by any two numbers is always the GCD
We write both 27 and x in the form of their prime factors

27=3^3
x=unknown

GCD=3 which means that x has exactly one 3 in its prime factorisation.(@himanshu...U may want to brush up on your LCM and GCD finding skills else u wouldn't be able to understand this)

So x is of the form 3a

Now, considering 100 and x
100=2^2*5^2
x=3a

GCD=2*5 meaning that x has to have exactly one 2 and one 5 among its prime factors else the GCD would be higher.

So x is of the form 3*2*5*b=30b

Now writing x and 2100 in the form of their prime factors
2100=2*2*3*5*5*7
x=2*3*5*b

GCD=2*3*5 or GCD=2*3*5*7......(as b could have 7 in its prime factorisation)

So the answer is either 30 or 210 i.e. either A or C. What is the OA?

knight247 · Answer

Hey Brent, Could you if possible go thru my post and help me filter out the incorrect option. I'd appreciate it. Thanks

Brent@GMATPrepNow · Answer

knight247 wrote:SL that is not the right answer.

The largest number that is divisible by any two numbers is always the GCD
We write both 27 and x in the form of their prime factors

27=3^3
x=unknown

GCD=3 which means that x has exactly one 3 in its prime factorisation.(@himanshu...U may want to brush up on your LCM and GCD finding skills else u wouldn't be able to understand this)

So x is of the form 3a

Now, considering 100 and x
100=2^2*5^2
x=3a

GCD=2*5 meaning that x has to have exactly one 2 and one 5 among its prime factors else the GCD would be higher.

So x is of the form 3*2*5*b=30b

Now writing x and 2100 in the form of their prime factors
2100=2*2*3*5*5*7
x=2*3*5*b

GCD=2*3*5 or GCD=2*3*5*7......(as b could have 7 in its prime factorisation)

So the answer is either 30 or 210 i.e. either A or C. What is the OA?

But cant B be another 2/3/5 instead of a 7? then the GCD would be 60/90/150 isnt it?

Please explain

thanks

update 9/14/2011 : never mind i got it

Brent@GMATPrepNow · Answer

imhimanshu wrote: Three is the largest number that an be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100
1 – 30
2- 70
3- 210
4 – 300
E – 700

In addition to having more than 1 correct answer, this question is worded poorly. The GMAT would never write "x divides evenly into y" since this could give one the impression that y divided by x must be an even number.

GMAT wording would say something like "3 is greatest common divisor of x and 27"

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

imhimanshu · Answer

This question is from Kaplan and the OA is C

imhimanshu · Answer

@ Knight 247, I did get this answer correct while giving my exam. However, I just wanted to see the different approaches in order to kill such questions. Thanks for the concern though ! appreciated !

deepsun · Answer

knight247 wrote:SL that is not the right answer.

The largest number that is divisible by any two numbers is always the GCD
We write both 27 and x in the form of their prime factors

27=3^3
x=unknown

GCD=3 which means that x has exactly one 3 in its prime factorisation.(@himanshu...U may want to brush up on your LCM and GCD finding skills else u wouldn't be able to understand this)

So x is of the form 3a

Now, considering 100 and x
100=2^2*5^2
x=3a

GCD=2*5 meaning that x has to have exactly one 2 and one 5 among its prime factors else the GCD would be higher.

So x is of the form 3*2*5*b=30b

Now writing x and 2100 in the form of their prime factors
2100=2*2*3*5*5*7
x=2*3*5*b

GCD=2*3*5 or GCD=2*3*5*7......(as b could have 7 in its prime factorisation)

So the answer is either 30 or 210 i.e. either A or C. What is the OA?

But cant B be another 2/3/5 instead of a 7? then the GCD would be 60/90/150 isnt it?

Please explain

thanks

update 9/14/2011 : never mind i got it

saketk · Answer

although we have 2 answers matching i.e. 30 and 210, we can safely eliminate 30 because the question is asking for the largest possible number.

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