What is the value of x? (1) x has exactly 3 factors. (2) 10

Question

What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45

nahid78 · Accepted Answer

1. Integers, whose square root are also integers, have odd number of factors.
2. square of prime has exactly 3 factors.

Bunuel · Answer

HINT:
1. What kind of integers have odd number of factors?
2. What kind of integers have 3 factors?

KS15 · Answer

(1) x has exactly 3 factors. Insufficient. We have can 3^2,5^2 and so on.
(2) 10 < x < 45. Clearly Insufficient

Using both statements, only one solution is possible i.e 5^2=25
Answer C

Bunuel · Answer

That's correct.

1. Positive perfect squares have odd number of factors: 1, 4, 9, 16, 25, ...
2. Only the squares of primes have 3 factors: 4, 9, 25, 49, ...

Nunuboy1994 · Answer

We can just apply a simple rule- the square of a prime has only 3 factors.

C

sarwarraza · Answer

Hi Bunuel,

We have 3 values between 10 and 45 which are perfect squares (16,25,36), So we have three values for X. Shouldn't the answer be E?

GMAThollic · Answer

But ONLY the perfect squares of prime factors have 3 factors.
for example: 25 (its factors are 1, 5 and 25)

16 has more than 3 factors (1, 2, 4, 8, 16)
same thing for 36

Only possible value for x is 25 -> Ans> C)

Sri07 · Answer

16 is square of 4 (4 is not prime)
36 is square of 6 (6 is not prime)
Only square of prime numbers have 3 factors.

If you are aware of the property of factors:

x^2= (WHERE X IS A PRIME NUMBER) number of factors will be 2+1 = 3

Therefore number of factors of 36 will be 6^2 = (2^2 * 3^2) = 3*3= 9 factors of 36 i.e 1,2,3,4,6,9,12,18 and 36

As per statement 1 any number all prime numbers squared will have 3 factors and can be X.

However, Statement 2 limits the values of "X" between 10 and 45.

Now, if we combine the 2 statements we will select the squared value of a prime number which when squared will lie between 10-45. Only such value is 5^2= 25

Hence, answer will be C because if you combine both Statement 1 and 2

bumpbot · Answer

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What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45

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