If 20x = 49y, which of the following must be true?

Question

I. x > y

II. x^2 > y^2

III. x/7 is an integer
 
A) I only
B) II only
C) III only
D) I and III
E) I, II, and III

hamm0 · Answer

I'd plug in numbers here. Try the weird ones i.e. 0, -1, 1/2, etc. as it does not note that x or y are integers.

Plugging in 0, We find that statement 1 and 2 are false. Looking at what is left, the solution must be C, Statement III is correct since there is no answer for "None of the above".

Good question, what is the source?

Carcass · Answer

hi Hamm0

As you can see is Veritas prep.

I attacked the question in that way tell me if is correct

20x = 49y

20   =   2^2   *5

49   =   7^2

so basically we would have the second one in the LHS and viceversa to balance the equation  BUT  we should consider also 0 because 0=0 so is equal ( but of course)

1) x > y true not always  7^2  >   2^2   *5  but we have also zero so x > y is not true

2)  x^2   >   y^2  we know that x and y are always positive so basically we can reduce the second statement to  x > y  and we know already insuff

3) \frac{x}{7}   = integer  yes  \frac{7^2}{7} =  integer always

C is correct

hamm0 · Answer

A quick glance over says that is correct. Just a different approach. Often the GMAT will do this - offer several ways to solve a problem. No brownie points for doing the more difficult, so if you recognize it, go with whichever you're faster/more comfortable.

Carcass · Answer

I asked here because I was not sure (better i'm sure at 99% ) in particular on statement 2. But if you said ok ...many Thanks

SVaidyaraman · Answer

We have 20x=49y
or x = 49y/20

I need not be true because x is greater than y only when y is positive.

II need not be true because both x and y can be zero. This applies to I also.

III also need not be true because x/7 =49y/140 = 7y/20. 
We can see that x/7 need not be an integer as for example in the case of y=1.

Bunuel · Answer

This is a flawed question. None of the options must be true.

Notice that 20x = 49y holds true if x=y=0, thus I and II are not always true.

As for III: if x=1 and y=20/49, then x/7 won't be an integer.

If the question were:
 If  x and y are integers  and 20x = 49y, which of the following must be true?

Then in this case III would be always true: RHS is a multiple of 7, thus LHS must also be a multiple of 7 and since 20 is not a multiple of 7, then x must be.

Hope it's clear.

Carcass · Answer

I perfectly understand what you say. Something it was not unclear to me either.

Though, my primary question was is me approach was correct generally speaking.

Thanks,

Regards

skamal7 · Answer

If 20x = 49y, which of the following must be true?

I. x > y
II. x^2 > y^2
III. x/7 is an integer

A)I only
B)II only
C) III only
D)I and III
E)I, II, and III

OA after some discussion

mau5 · Answer

For x = 1,y = 20/49 and x>y. However, for x=-49,y = -20 and y>x. I is clearly not the right answer.
For y=0, x=0. Thus, even II doesn't hold good.
x/7 = 7y/20. For y=0, x/7 is an integer, however for y=1, it is not.
None of the options are (must be)true

Zarrolou · Answer

If 20x = 49y, which of the following must be true?

I. x > y
II. x^2 > y^2
III. x/7 is an integer

Just pick  x=0  and  y=0

Options I and II are false (0 is not  > 0 ), only III is true. And holds true for each value of x because  4*5*x=7*7*y  so or x=0 or x is a multiple of 7, in both cases  \frac{x}{7}  is an integer.
 C

PS: given that x, y are integers. Otherwise none must be true

Edit post: 
A)I only
B)II only
C) III only
D)I and III
E)I, II, and III

These are Veritas possible answers. The "none" option is not available, as you see. So we must assume that are integers and that the question is not complete (it must specify that x,y are integers). However the question itself , because x and y could be fractions (no integers) has an hypothetical "F)none of the above" as correct answer. No doubt.

The question is incomplete

skamal7 · Answer

if x =1/20 and y=1/49 still the equation holds right?

SO at this point of time option 3 also goes wrong...Any opinion on this?

mau5 · Answer

That is not true. It has not been mentioned that x and y are integers.

Bunuel · Answer

Merging similar topics.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If 20x = 49y, which of the following must be true?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards