Question: w and k are Integers

Comment on w and k are Integers

This question is not clear to me. If w = 42; then K= (340042/(2*2*5*7*17) = 142.87; How K is an integer?

Can you please explain?
greenlight-admin's picture

In the expression 3400w, the variable w does not represent a digit (or digits in your example). For more on this, watch: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

The variable w represents a value that is MULTIPLIED by 3400. In other words, 3400w is equal to 3400 TIMES some number (called w)

So, if w = 42; then k = (3400)(42)/(2)(2)(5)(7)(17)
= 142800/2380
= 60

I solved the question by testing the answer choices.

Answers a) through d) were all not whole integers. Ex- C) was 3400(34) 115,600/ 2380=48.57 while the only answer choice which divided as a whole integer was E) 142,800/2380= 60
greenlight-admin's picture

That works too! :-)

Hi Brent ,

I found one of the similar question but in different way
please help me in the approach

if I just change the question as

k=3400w/2*2*5*7*17
so we get 2380/3400w

as the last digit of the numerator is 0 ,
we should find a number that is divisible by 2,5,10

is this the right approach

Thanks
greenlight-admin's picture

That approach can (and did) yield unintended results.
For this question I strongly recommend that you find a prime factorization of 3400, and then eliminate some prime factors from the numerator and denominator (as I did in the solution)

k = 3400w/(2)(2)(5)(7)(17)
= (2)(2)(2)(5)(5)(17)(w)/(2)(2)(5)(7)(17)
= (2)(5)(w)/(7)

From here we can see that, in order for k to be an integer, it must be the case that w is a multiple of 7.

For this reason the correct answer is E, since 42 is the only answer choice that is a multiple of 7.

Very good question. I solved it simply by reducing the fraction to 10W / 7, then just test the answers. 42 would be 420 / 7, which works great.

Add a comment

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Let me Know

Have a suggestion to make the course even better? Email me today!

Free “Question of the Day” emails!