For nonnegative integers x and y, 30x = 49y. Which of the following

Question

For nonnegative integers x and y, 30x = 49y. Which of the following must be true?

I. x > y
II. y/10 is an integer.
III.  \frac{\sqrt{x}}{7}  is an integer.
 
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

Bunuel · Accepted Answer

30x = 49y --> x is a nonnegative multiple of 49 (0, 49, 98, ...) and y is a nonnegative multiple of 30 (0, 30, 60).

I. x > y. Not necessarily true. It's possible that x = y = 0.

II. y/10 is an integer. Since y is a multiple of 30, then it must be a multiple of 10 too. So, this statement must be true.

III.  \frac{\sqrt{x}}{7}  is an integer. Not necessarily true, consider x = 98.

Answer: B.

PareshGmat · Answer

30x = 49y,

so x = 49 & y = 30 OR

x = 49*2 & y = 30*2 and so on............

x > y >> This will always hold true

\frac{y}{10}  is an integer >> Again, this will always hold true

\frac{\sqrt{x}}{7}  >> Not necessary; for x = 98, this condition will fail

Answer = D

Can you please check the OA?

push12345 · Answer

I) not necessary as x and y can be zero

II)y needs to be multiple of 10
.so must be condition

III) if x=49*5
Y=30*5
Both sides equal but
√x/7 is not integer

So only II is true

Posted from my mobile device

Fdambro294 · Answer

The key constraint to keep track of is that X and Y are “non-negative integers”

This means both X and Y can equal 0

Given: 30x = 49y

2*3*5*x = 7*7*y

Case 1: x = 0 = y

Case 2: if x and y are positive integers, since neither of the coefficients contain any of the Prime Factors of the other coefficient, all we know for sure is that:

X must be a multiple of (7 * 7)

and

Y must be a multiple of (2*3*5)

W.O.T.F. Must be true?

I. Does not have to be true.

X = 0 = Y

II. Y/10 = integer

Either Y = 0 and 0 is a multiple of every integer

or

if Y is a positive integer, we know that Y must be a Multiple of (2*3*5) - which means it must be evenly divisible by 10

II must be true

III.

X only has to be a multiple of (7*7) ——X does not have to be a Perfect Square

Example:

X can = (7 * 7) * 2

And

Y can = (2*3*5) * 2

30x = 49y ———

30x = (2*3*5) * (7*7*2) = (2)^2 * (3) * (5) * (7)^2

49y = (7*7) * (2*3*5*2) = (2)^2 * (3) * (5) * (7)^2

And the given equation would be satisfied.

III does not have to be true.

II is the only one that must be true

Posted from my mobile device

bumpbot · Answer

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For nonnegative integers x and y, 30x = 49y. Which of the following

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For nonnegative integers x and y, 30x = 49y. Which of the following

Prep Toolkit

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