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?
MGMAT 2 -DS question
This topic has expert replies
-
- Legendary Member
- Posts: 2467
- Joined: Thu Aug 28, 2008 6:14 pm
- Thanked: 331 times
- Followed by:11 members
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)
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)