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# If a & b are positive integers, , is a/b a terminating decimal number?

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Director
Joined: 02 Oct 2017
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If a & b are positive integers, , is a/b a terminating decimal number?  [#permalink]

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07 Nov 2018, 01:18
1
1
4
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Difficulty:

45% (medium)

Question Stats:

55% (01:04) correct 45% (01:16) wrong based on 97 sessions

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If a & b are positive integers, , is a/b a terminating decimal number?

i) b is a factor of 50

ii) b/a is an integer
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Joined: 02 Aug 2009
Posts: 8289
Re: If a & b are positive integers, , is a/b a terminating decimal number?  [#permalink]

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09 Nov 2018, 11:52
If a & b are positive integers, , is a/b a terminating decimal number?

i) b is a factor of 50
So denominator will have 1,2,5,10,25,50 and each of them will result in terminating decimal, as any power of 2 and 5 or multiples of just 2 and 5 leave a terminating decimal
Sufficient

ii) b/a is an integer
If a=2 and b=4... Yes
If a =2 and b=6... No
Insufficient

A
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Re: If a & b are positive integers, , is a/b a terminating decimal number?  [#permalink]

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09 Nov 2018, 12:29
Had a not been a positive inteer, E would have been correct.
Missed it ! @
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If a and b are positive integers, is a/b a terminating decimal number?  [#permalink]

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28 Nov 2019, 06:05
If a and b are positive integers, is a/b a terminating decimal number?

(1) b is a factor of 50.

(2) b/a is an integer.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: If a & b are positive integers, , is a/b a terminating decimal number?  [#permalink]

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28 Nov 2019, 08:49
For a/b to be a terminating decimal, in reduced fraction a/b, b must contain twos or fives

1) b is a factor of 50 --> $$5^2*2$$ SUfficient
2) b can be other integers than 2 or 5. Not sufficient

IMO
ans: A
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Re: If a & b are positive integers, , is a/b a terminating decimal number?  [#permalink]

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29 Nov 2019, 12:46
push12345 wrote:
If a & b are positive integers, , is a/b a terminating decimal number?

i) b is a factor of 50

ii) b/a is an integer

Analyzing the question:
This only depends on b. If b has prime factors such as 3, 7, 11 etc it is not terminating. In other words, if b has only prime factors of 2 and 5 then a/b is terminating.

Statement 1:
Prime factors of 50 include only 2 and 5. Dividing integers by 2 or 5 do not cause any repeating decimals, so the integers still terminate. Sufficient.

Statement 2:
This tells us the prime factors of $$a$$ include only 2 and 5 but since we want to know something on $$b$$ this is insufficient.

Ans: A
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Re: If a & b are positive integers, , is a/b a terminating decimal number?  [#permalink]

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29 Nov 2019, 22:52
push12345 wrote:
If a & b are positive integers, , is a/b a terminating decimal number?

i) b is a factor of 50

ii) b/a is an integer

To get a terminating decimal, the denominator must be must be contain 2 or 5 or both.
(1) b will be either 2 or 5 or both. Sufficient
(2) value of b is not provided. Insufficient

A is correct.
Re: If a & b are positive integers, , is a/b a terminating decimal number?   [#permalink] 29 Nov 2019, 22:52
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