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What is the units digit of x?

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Math Expert
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What is the units digit of x?  [#permalink]

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26 Apr 2016, 23:15
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45% (medium)

Question Stats:

59% (01:07) correct 41% (01:23) wrong based on 115 sessions

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What is the units digit of x?

(1) $$\frac{x}{5^a2^b3^c}=k$$, where k is an integer and a, b, and c are positive integers.

(2) a = 2, b = 3, and c = 4

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Posts: 7036
What is the units digit of x?  [#permalink]

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27 Apr 2016, 06:22
2
Bunuel wrote:
What is the units digit of x?

(1) $$\frac{x}{5^a2^b3^c}=k$$, where k is an integer and a, b, and c are positive integers.

(2) a = 2, b = 3, and c = 4

Nothing much in Q stem so lets see the statements--
(1) $$\frac{x}{5^a2^b3^c}=k$$, where k is an integer and a, b, and c are positive integers.
if denominator has even ONE 2 and 5, x will become a multiple of 10 and hence units digit will be 0..
if ONLY 5 is there and NO 2s, x will be multiple of 5, and hence units digit will be 5
But a, b and c are positive integers so >0..
our units digit will be 0
suff

(2) a = 2, b = 3, and c = 4
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the units digit of x?  [#permalink]

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27 Apr 2016, 06:32
1
chetan2u wrote:
Bunuel wrote:
What is the units digit of x?

(1) $$\frac{x}{5^a2^b3^c}=k$$, where k is an integer and a, b, and c are positive integers.

(2) a = 2, b = 3, and c = 4

Nothing much in Q stem so lets see the statements--
(1) $$\frac{x}{5^a2^b3^c}=k$$, where k is an integer and a, b, and c are positive integers.
if denominator has even ONE 2 and 5, x will become a multiple of 10 and hence units digit will be 0..
if ONLY 5 is there and NO 2s, x will be multiple of 5, and hence units digit will be 5
Insuff

(2) a = 2, b = 3, and c = 4
insuff

combined..
we know that x is a multiple of 10 and hence unit's digit is 0..
Suff

C

Hi Chetan,

Since a, b and c are positive, the denominator contains atleast one 2, 5 and 3 right?
Also k is an integer. So x must contain a 0 in the units digit. Shouldn't the answer be A?
Math Expert
Joined: 02 Aug 2009
Posts: 7036
Re: What is the units digit of x?  [#permalink]

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27 Apr 2016, 06:40
Vyshak wrote:
chetan2u wrote:
Bunuel wrote:
What is the units digit of x?

(1) $$\frac{x}{5^a2^b3^c}=k$$, where k is an integer and a, b, and c are positive integers.

(2) a = 2, b = 3, and c = 4

Nothing much in Q stem so lets see the statements--
(1) $$\frac{x}{5^a2^b3^c}=k$$, where k is an integer and a, b, and c are positive integers.
if denominator has even ONE 2 and 5, x will become a multiple of 10 and hence units digit will be 0..
if ONLY 5 is there and NO 2s, x will be multiple of 5, and hence units digit will be 5
Insuff

(2) a = 2, b = 3, and c = 4
insuff

combined..
we know that x is a multiple of 10 and hence unit's digit is 0..
Suff

C

Hi Chetan,

Since a, b and c are positive, the denominator contains atleast one 2, 5 and 3 right?
Also k is an integer. So x must contain a 0 in the units digit. Shouldn't the answer be A?

Hi Vyshak,
you are absolutely correct..
I missed out on POSITIVE and fell for the trap..
Kudos..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the units digit of x?  [#permalink]

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19 Nov 2016, 01:35
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Re: What is the units digit of x?  [#permalink]

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26 Aug 2018, 02:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the units digit of x? &nbs [#permalink] 26 Aug 2018, 02:06
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