MGMAT 2 -DS question

[vinny_r78]

This is my first post in the forum.

If a, b, c, d and e are integers and p = 2^a*3^b and q = 2^c*3^d*5^e, is p/q a terminating decimal?

(1) a > c
(2) b > d

^ denotes power
* denotes multiplication

Could someone provide the answer and the reasoning?

I find this question very tough. Can someone tell me whether this kind of question would come in original GMAT?

[cramya]

Quite possible!

I think the concept behind terminating decimals is that if a denominator of a fraction can be expressed as non negative powers of 2 and 5

hypothetical example:

It could be 2^3 * 5 ^ 0 or 5^2 * 2^0 or 5^3 * 2^10 to name a few (IMO we can make up the 0 power part for either 2 or 5 so it basically boils down to if the denominator can be expressed as 2^some power or 5 ^ somepower - someone feel free to chip in on this part if u feel its misstated but I am pretty sure )

If a, b, c, d and e are integers and p = 2^a*3^b and q = 2^c*3^d*5^e, is p/q a terminating decimal?

Stmt I
(1) a > c No info about exponents of 3

We dont know if b>d (i.e even if 2 powers in the denominator cancels it can still be terminating decimal if the 3 powers in the denominator cancels also - per what i said in the beginning before this problem) which is really what we need to answer the question if the denominator can be expressed as powers of 5 or 2

(2) b>d

We know the 3^d cancles out leaving the denominator as 2^somepower * 5^somepower

Yes its a terminating decimal

SUFF

B)

[austin]

Terminating decimals: 1/2, 1/4, 1/5, 1/8, 1/10 etc ......

Finite numbers after the decimal

1/3 = 0.333333....Non -terminating..same with 1/6