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# What is the units digit of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
What is the units digit of x?  [#permalink]

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26 Apr 2016, 06:38
3
2
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Difficulty:

55% (hard)

Question Stats:

58% (01:20) correct 42% (01:21) wrong based on 119 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.

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

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

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26 Apr 2016, 09:33
3
Units digit of x = ?

St1: x/(5^a * 2^b * 3^c) is an integer
$$x = (5^a * 2^b * 3^c) * k$$
If a, b, c = 0 and k = 1 then Units Digit = 1
If a, b, c = 1 and k =1 then Units Digit = 0
Not sufficient

St2: a = 2, b = 3, and c = 4 --> Clearly insufficient

Combining St1 and St2: $$x = (5^2 * 2^3 * 3^4) * k$$
Since x has atleast one 5 and 2, Units Digit will be 0.
Sufficient

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

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27 Apr 2016, 03:21
Vyshak wrote:
Units digit of x = ?

St1: x/(5^a * 2^b * 3^c) is an integer
$$x = (5^a * 2^b * 3^c) * k$$
If a, b, c = 0 and k = 1 then Units Digit = 1
If a, b, c = 1 and k =1 then Units Digit = 0
Not sufficient

St2: a = 2, b = 3, and c = 4 --> Clearly insufficient

Combining St1 and St2: $$x = (5^2 * 2^3 * 3^4) * k$$
Since x has atleast one 5 and 2, Units Digit will be 0.
Sufficient

Marked the answer as E considering the UNITS digit for K instead of X...highly tricky sir...
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Re: What is the units digit of x?  [#permalink]

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24 Nov 2016, 04:41
Great Question
Here is what i did =>
Clearly statements 1 and 2 are insufficient on there own.
Combining them we can say that x must have both 2 and 5 as its prime factors.
Hence the Unit digit of x must be zero.
Hence C
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Re: What is the units digit of x?  [#permalink]

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07 Feb 2019, 23:26
Bunuel wrote:
What is the units digit of x?

(1) $$\frac{x}{5^a2^b3^c}=k$$, where k is an integer.

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

Keyword => UD of x

Nothing special to do

from 1 , if k is an integer, this will mean that k will be absorbing the denominator completely.
But we dont how numerator is present, it can have more number of 5, 2 or 3

from 2, we dont get any information

Combination gives us the split among a, b and c.

When calculated will give us an unique value.

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

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15 Sep 2019, 12:15
stonecold wrote:
Great Question
Here is what i did =>
Clearly statements 1 and 2 are insufficient on there own.
Combining them we can say that x must have both 2 and 5 as its prime factors.
Hence the Unit digit of x must be zero.
Hence C

Hi,

Would you be more specific on why S2 is insufficient?
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What is the units digit of x?  [#permalink]

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15 Sep 2019, 14:35
Lol this an old post ,about 3years ago guess the user is not around.
Now coming to your question (st2) is not suff. because we don’t know what x is , x can be 5 where unit digit is 5, x can be 43 where unit digit is 3 .Info about a,b,and c is irrelevant here. (value is not consistent hence insufficient)
stonecold wrote:
Great Question
Here is what i did =>
Clearly statements 1 and 2 are insufficient on there own.
Combining them we can say that x must have both 2 and 5 as its prime factors.
Hence the Unit digit of x must be zero.
Hence C

Hi,

Would you be more specific on why S2 is insufficient?

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What is the units digit of x?   [#permalink] 15 Sep 2019, 14:35
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