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## Any decimal that has only a finite number

This topic has 2 expert replies and 1 member reply

### Top Member

lheiannie07 Legendary Member
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#### Any decimal that has only a finite number

Thu Sep 21, 2017 6:22 am
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?

(1) k = 3

(2) j is an odd multiple of 3.

Badly need help from experts here. How will i come up with the right statement?

OA C

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
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GMAT Score:
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Thu Sep 21, 2017 7:50 pm
Hi lheiannie07,

We're told that J and K are positive integers. We're asked if J/K can be expressed as a terminating decimal. This is a YES/NO question. We can solve it by TESTing VALUES.

1) K = 3

IF.... J = 3, then J/K = 3/3 = 1.0 and the answer to the question is YES.
J = 4, then J/K = 4/3 = 1.333333333etc. and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) J is an odd multiple of 3.

IF.... J = 3 and K = 3, then J/K = 3/3 = 1.0 and the answer to the question is YES.
J = 3 and K = 9, then J/K = 3/9 = 0.333333333etc. and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know
K = 3
J is an odd multiple of 3 (such as 3, 9, 15, 21, etc.)
Since J is a multiple of 3, dividing that number by 3 (the value of K) will ALWAYS lead to an integer. By definition, J/K will ALWAYS be a terminating decimal and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
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Tue Jan 16, 2018 5:06 pm
lheiannie07 wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?

(1) k = 3

(2) j is an odd multiple of 3.
\

We need to determine whether j/k is a terminating decimal given that j and k are positive integers. One thing we should keep in mind is that a fraction (in lowest terms and with a denominator greater than 1) can be expressed as a terminating decimal if and only if the denominator comprises prime factors of only 2 and/or 5. For example, 3/10 and 3/15 = 1/5 are terminating decimals, whereas 3/7 and 3/9 = 1/3 are not. On the other hand, if the denominator is 1, the fraction is always a terminating decimal as long as the numerator is an integer.

Statement One Alone:

k = 3

Depending on the value of j, j/k may or may not be a terminating decimal. For example, if j = 1, then j/k = 1/3 is not a terminating decimal. On the other hand, if j = 3, then j/k = 3/3 = 1/1 = 1 is a terminating decimal. Statement one is not sufficient to answer the question.

Statement Two Alone:

j is an odd multiple of 3.

Depending on the value of k, j/k may or may not be a terminating decimal. For example, if j = 3 and k = 7, then j/k = 3/7 is not a terminating decimal. On the other hand, if j = 3, and k = 3, then j/k = 3/3 = 1/1 = 1 is a terminating decimal. Statement two is not sufficient to answer the question.

Statements One and Two Together:

Since j is an odd multiple of 3, and k = 3, j/k is always an odd integer. Thus, j/k is a terminating decimal.

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Scott Woodbury-Stewart Founder and CEO

### Top Member

lheiannie07 Legendary Member
Joined
07 Sep 2017
Posted:
710 messages
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Wed Jan 10, 2018 12:14 am
Rich.C@EMPOWERgmat.com wrote:
Hi lheiannie07,

We're told that J and K are positive integers. We're asked if J/K can be expressed as a terminating decimal. This is a YES/NO question. We can solve it by TESTing VALUES.

1) K = 3

IF.... J = 3, then J/K = 3/3 = 1.0 and the answer to the question is YES.
J = 4, then J/K = 4/3 = 1.333333333etc. and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) J is an odd multiple of 3.

IF.... J = 3 and K = 3, then J/K = 3/3 = 1.0 and the answer to the question is YES.
J = 3 and K = 9, then J/K = 3/9 = 0.333333333etc. and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know
K = 3
J is an odd multiple of 3 (such as 3, 9, 15, 21, etc.)
Since J is a multiple of 3, dividing that number by 3 (the value of K) will ALWAYS lead to an integer. By definition, J/K will ALWAYS be a terminating decimal and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich
Thanks a lot!

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