Lesson: Properties of Fractions - Part II

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Hi Brent,
For this question https://gmatclub.com/forum/if-0-y-x-then-which-of-the-following-is-233173.html
can we use the approach of testing some values?
Since x > y > 0 ,
let x=2 and y=1
27x+23y / 3x+2y = 54 + 23 / 6 + 2 = 77 / 8 =9.625
Let x = 3 and y =2
81+46 / 9+4 = 127/13=9.76
let x= 5 and y =4, result 9.86
let x = 13 and y =2, result 9.23
I just tested these values, but not sure if at some values the result will deviate from 9.
Thanks for your help.
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-0-y-x-then-which-of-the-following-is-23317...

Hi Aladdin,
Your approach is a good idea. The only problem is that this strategy only gives us the FEELING that the expression COULD equal 9.2

However, it's hard to have any certainty about whether or not it's possible to get the other two values (8.7 and 10.8)

That said, if you don't spot any other approach, this will at least help give you an idea of what the correct answer might be.


hi brent,

For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

In this question, I understand the answer is 3, used divisibility to ans the question. But I can't understand why it is incorrect, can't integer be a decimal?
gmat-admin's picture

An integer is a whole number: . . . -3, -2, -1, 0, 1, 2, 3, . . .
So, for example, the decimal 3.2 is not an integer.

Here's my full solution: https://gmatclub.com/forum/for-which-of-the-following-values-of-n-is-100...


For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(18)/h(10) ?

(A) 1.8
(B) 3
(C) 6
(D) 18
(E) 60

Hi Brent, can you please share step by step method to solve this?
gmat-admin's picture

I'm happy to help.
Here's my step-by-step solution: https://gmatclub.com/forum/for-all-even-integers-n-h-n-is-defined-to-be-...


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