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What is the units digit of x?

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

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New post 26 Apr 2016, 05:38
3
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

53% (01:24) correct 47% (01:21) wrong based on 70 sessions

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

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New post 26 Apr 2016, 08:33
2
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

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

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New post 27 Apr 2016, 02:21
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

Answer: C


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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New post 24 Nov 2016, 03:41
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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New post 07 Feb 2019, 22:26
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] 07 Feb 2019, 22:26
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