What is the units digit of x?

Question

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

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

Kurtosis · Answer

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

Balajikarthick1990 · Answer

Marked the answer as E considering the UNITS digit for K instead of X...highly tricky sir...

stonecold · Answer

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

KanishkM · Answer

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

auradediligodo · Answer

Hi,

Would you be more specific on why S2 is insufficient?

Staphyk · Answer

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)

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exc4libur · Answer

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

(a,b)=1:\frac{x}{10*3^c}…units(x)=0 
 (a,b)=0:\frac{x}{3^c}…units(x)=anything

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

(1)(2)   sufic

\frac{x}{5^22^33^4}=\frac{x}{10*2*3^4}…units(x)=0

Ans (C)

esonrev · Answer

Don't really understand how this is sufficient after combining the axioms... could someone explain?

Staphyk · Answer

Hello where lies your confusion?What answer did you pick for this question so that I explain why is/not wrong

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vishalsinghvs08 · Answer

Bunuel   Staphyk   Kurtosis

i still dont understand this.

x can be 5^ax2^bx3^cxm(any other number) --- In this case the unity digit will be m because numerator and denominator will cancel each other except for the other variable "m"
or

x can be 5^ax2^bx3^c --- in this case the entire numerator and denomintor will cancel each other completely. The unit digit will be one

or 
x can be bigger exponent value of 5,2,3 or any combinatior of them. In this case the unity digit will be zero

What is the units digit of x?

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GMAT Data Sufficiency (DS) Questions

What is the units digit of x?

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