hemant_rajput wrote:Three is the largest number that can 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 2,100?
a.30
b.70
c.210
d.300
e.700

[spoiler]OA:C[/spoiler]
what does it mean when you say 3 divide evenly into 27 and x?

what does it mean when you say 3 divide evenly into 27 and x?
The wording here could be improved. 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.
In everyday, informal speech, saying that x divides evenly into y is the same as saying that x is a divisor of y.

For this question, the GMAT test-makers would probably write something like "3 is greatest common divisor of x and 27"


A fast approach here is 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

hemant_rajput wrote:thanks Brent.

when we say x divides y evenly, can it also mean that y is even no?

No, we can't conclude that y is even. For example, we could say that 3 divides evenly into 15.

As I said, though, an official GMAT question would never say "divides evenly into"

Cheers,
Brent