Manhattan GMAT Challenge Problem

[KevinFitzgerald]

Most Manhattan GMAT students are trying to break the 700 barrier. As a result, we've developed our own math problems written at the 700+ level; these are the types of questions you'll WANT to see, when you are working at that level. Try to solve this 700+ level problem (I'll post the solution next Monday).

Question:
When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?

I. 15.15
II. 18.16
III. 17.17

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

[Sramits]

Originally Posted by KevinFitzgerald

Most Manhattan GMAT students are trying to break the 700 barrier. As a result, we've developed our own math problems written at the 700+ level; these are the types of questions you'll WANT to see, when you are working at that level. Try to solve this 700+ level problem (I'll post the solution next Monday).

Question:
When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?

I. 15.15
II. 18.16
III. 17.17

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

answer 3.....................

[deepeshkothari]

Originally Posted by KevinFitzgerald

Most Manhattan GMAT students are trying to break the 700 barrier. As a result, we've developed our own math problems written at the 700+ level; these are the types of questions you'll WANT to see, when you are working at that level. Try to solve this 700+ level problem (I'll post the solution next Monday).

Question:
When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?

I. 15.15
II. 18.16
III. 17.17

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

i think the answer is D.....
we can make two equations for each option..
eg.
x=15y-60
and
x/y=15.15
so..
1st two options satisfy the eq's...

[bdsam]

My Answer is D too ...

See when we divide x/y the remainder is 60

Now Case 1: 15.15
which means, 0.15 * y = 60 => y = 400 [An Integer, so this is possible]

Similarly, Case 2: 18.16
which means, 0.16 * y = 60 => y = 375 [An Integer]

Again, Case 3: 17.17
which means, 0.17 * y = 60 => y = 352.94 [Not an Integer, so not possible]

So, I & II are Possible ....

[ahmadazeem777]

I will also go with D ... & agree with the explanation given by bdsam

[KevinFitzgerald]

If the integer x divided by y has a remainder of 60, then x can be expressed as:
x = ky + 60, where k is an integer (i.e. y goes into x k times with a remainder of 60)

We could also write an expression for the quotient x/y:
x = k + 60
y y

Notice that k is still the number of times that y goes into x evenly.

60

y

is the decimal portion of the quotient, i.e. the remainder over the divisor y.



The first step to solving this problem is realizing that k, the number of times that y goes into x evenly, can be anything for this question since we are only given a value for the remainder. The integer values before the decimal point in answers I, II and III are irrelevant.

The decimal portion of the possible quotients in I, II and III are another story. From the equation we have above, for a decimal to be possible, it must be something that can be expressed as 60/y, since that is the portion of the quotient that corresponds to the decimal. But couldn't any decimal be expressed as 60 over some y? The answer is NO because we are told in the question that y is an integer.

Let's look at answer choice I first. Does
60 =.15, where y is an integer?
y

If we rearrange this equation, we get: Does
60 =y, where y is an integer?
.15

This question is tantamount to asking if 60 is divisible by 0.15 or if 6000 is divisible by 15?
6000 IS divisible by 15 because it is divisible by 5 (ends in a 0) and by 3 (sum of digits, 6, is divisible by 3)
Therefore, answer choice I is CORRECT.

Using the same logic for answer choice II, we must check to see if 6000 is divisible by 16.
6000 IS divisible by 16 because it is can be divided by 2 four times: 3000, 1500, 750, 375.
Therefore, answer choice II is CORRECT.

6000 IS NOT divisible by 17 because 17 is prime and not part of the prime make-up of 6000.
Therefore answer choice III is NOT CORRECT.

Therefore the correct answer is D, I and II only.