When 15x is divided by 2y, the quotient is x

Question

When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x 
D) x < 3
E) y < 8

*kudos for all correct solutions

vitaliyGMAT · Accepted Answer

Hi

We have:

15x = 2y*x + x

14x = 2x*y

y = 7

Answer E

tapabrata · Answer

When A is divided by B and the quotient is Q and the remainder is R, then
A=B*Q+R ... equation 1

For our case, 
A=15x, B=2y , Q=x and R=x

Putting all the values in equation 1, we get
 15x=2y*x+x
=>14x=2xy
=> y=7 which is less than 8

Answer E

gracie · Answer

15x=2xy+x
y=7
testing possible values of x,
x=any positive integer≥1
thus, A,B,C and D are false,
and only y<8 is true
E

BrentGMATPrepNow · Answer

There's a nice rule that say, "  If N divided by D equals Q with remainder R, then N = DQ + R  "
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

------NOW ONTO THE QUESTION------------------------------

When 15x is divided by 2y, the quotient is x, and the remainder is x.  
Applying the above rule, we can write: 15x = (2x)(y) + x
Subtract x from both sides to get: 14x = 2xy
Divide both sides by 2x to get: y = 7

Answer: E

Adityagmatclub · Answer

Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??

Bunuel · Answer

If it were:  when 15 is divided by 2y, the quotient is x, and the remainder is x.

Then,  15 = 2xy + x = x(2y + 1)

In this case, (x, y) can be (1, 7) or (3, 2) only. So, both A and E will be correct.

pulkitaggi · Answer

(5,1) also. Right?

Bunuel · Answer

No, x = 5 and y = 1 does not work. Though these numbers fit the formula they do not satisfy the conditions given in the stem: 15 divided by 2y = 2 gives the quotient 7 and the remainder of 1, not 5 and 5. The point is that the remainder (x= 5 in this case) cannot be more than the divisor (2y = 2 in this case)

Inten21 · Answer

We know that --> Dividend = Quotient * Divisor + Remainder

we have, 15x = (2x) * y + x
14x = 2x * y
y = 14x/2x
y = 7

y < 8 
 Therefore, E

GMATINSECT · Answer

We can use this formula to get this one , otherwise taking numbers will take too long ,as I tried taking numbers for this one .
Dividend = Divisor * Quotient + Remainder 
Then , it comes 
15x = 27*x + x 
7 = Y 
From options E Y < 8 (Y less than 8)

ScottTargetTestPrep · Answer

We can create the equation:

15x/(2y) = x + x/(2y)

15x = 2yx + x

14x = 2yx

Recall that x is a positive integer; thus we can divide each side by x:

14 = 2y

7 = y

Answer: E

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When 15x is divided by 2y, the quotient is x

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