Question: 2520k is a Perfect Square

Comment on 2520k is a Perfect Square

Good evening!
My question might be ridiculous, but I got a bit confused and hope, you'll help me to figure the situation out.
Approaching this task, I was also relying on a rule of an even number of each prime in factorization. Thus, I thought, if a number is divisible by 5, it should be at least divisible by a square of 5 to satisfy the condition. However, it didn't lead me to a solution and I wonder why.
Thanks in advance for your answer :)
gmat-admin's picture

You are absolutely right. We can already see that 2520k is divisible by 5, and since we're told that 2520k is a square, we can correctly conclude that 2520k is divisible by 5², which means there must be TWO 5's in the prime factorization of 2520k

Can you provide more details on the approach you took?

I'm so sorry, only now I realise that my problem is coming from a wrong interpretation of the task. Looking at 2520k, I assumed that k represents 2-3 missing digits and worked with such numbers as 252035, 252070, etc. I understand now that k stands for a factor of a perfect square and can tackle the question
gmat-admin's picture

Ah, I can see how one might interpret the question that way.
If that were the intent of an official GMAT question, there would definitely be some information that states that the variable represents a digit.

is there a faster way to factor 2520? It took me about 45 seconds doing it the ol' fashion way.
gmat-admin's picture

Great question.
When using the ol' timey approach, try to find LARGE values that divide into the initial value.

For example, I know that 20 is a divisor of 2500, and 20 is a divisor of 20
So, 20 is a divisor of 2500 + 20 (aka 2520)
Se get: 2520 = (20)(126)
At this point, it's relatively easy to break down 20 and 126

Compare this to finding small values that divide into 2520
For example....
2520 = (2)(1260)
= (2)(2)(630)
= (2)(2)(3)(210)

Keep practicing your prime factorizing. You'll get faster!


Thanks, Brent. I started with 10 since I followed the ending unit "0" and 10 rule from a earlier lesson. I'll go bigger next next time.
gmat-admin's picture

You know what they say: "Go big or go home" (I can only assume "they" are talking about prime factorization)

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