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:

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

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

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.

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