If the product of the digits of a two-digit number x is 12, what is

Question

If the product of the digits of a two-digit number x is 12, what is the value of x?

(1) The units digit of x is a prime number.
(2) x is even.

Kurtosis · Answer

12 = 2 * 6 or 3 * 4
Possible values of x: 26, 62, 34, 43

St1: The units digit of x is a prime number --> x can be 62 or 43 --> Not Sufficient

St2: x is even --> x can be 26, 62 or 34 --> Not sufficient

Combining St1 and St2 --> x = 62
Sufficient

Answer: C

OptimusPrepJanielle · Answer

Product of two digits of a number = 12
Therefore number can be = 26, 34, 43, 62

Statement 1: The units digit of x is a prime number
For both 43 and 62, units digit is prime.
Insufficient

Statement 2: x is even
For 26, 62 and 34, x is even
Insufficient

Combining both:
last digit is prime and x is even.
Only 62 satisfies both the conditions.
Sufficient

Option C

MathRevolution · Answer

If the product of the digits of a two-digit number x is 12, what is the value of x?

(1) The units digit of x is a prime number.
(2) x is even.

If we look at the original condition, we get x=26,34,43,62. There is 1 variable (x), and in order to match the number of variables to the number of equations, we need 1 more equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the answer.
For the condition 1), since x=43, 62, the answer is not unique and the condition is not sufficient.
For the condition 2), since x=26, 62, the answer is not unique and the condition is not sufficient.
Using both the condition 1) and the condition 2), we get x=62. The answer is unique and the condition is sufficient. Therefore, the correct answer is C.

l For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

stonecold · Answer

The only case that will satisfy the two statements is x=62 
hence C

Archit3110 · Answer

possible value pf x = 26,62,43 & 34
#1
x= 62 & 43 insufficient
#2
x is even 26,62,34
insuffieint
from 1 & 2
62
IMO C

If the product of the digits of a two-digit number x is 12, what is

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GMAT Data Sufficiency (DS) Questions

If the product of the digits of a two-digit number x is 12, what is

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