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# x/y=5.35 If x and y are positive integers, then what is the

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Senior Manager
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x/y=5.35 If x and y are positive integers, then what is the  [#permalink]

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05 Oct 2010, 18:39
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Question Stats:

41% (02:01) correct 59% (02:29) wrong based on 263 sessions

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x/y=5.35
If x and y are positive integers, then what is the value of x?

(1) When y is divided by x, the remainder is 20.

(2) When x is divided by y, the remainder is 7.
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28 Oct 2011, 11:01
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Your reasoning worked to reach D in this case, but we have to be careful with setups like this. From the statements alone, we just know that x/y = 107/20. x & y could be any multiple of those numbers, and we don't necessarily want to try to confirm that they fit those particular values.

To solve this, we need to know that the fractional part is equal to the remainder over the divisor. Since statement 2 uses the same setup as our original equation, let’s start there:

2) .35=7/y
.35y=7
(7/20)y=7
y=7(20/7)
y=20

Once we know that y=20, we can plug into our original equation:

x/y=5.35
x/20=5.35
x=107
Sufficient

1) We can’t use the same approach for statement 1, because we don’t know the fractional part when y is divided by x. However, we might notice that since x/y >1, y/x must be less than 1. In other words, if y goes into x more than 5 times, we know that x is bigger than y, so y can’t go into x at all!

If x goes into y zero times, then y/x = 0 r 20. Therefore, the remainder *is* our value for y.
y=20

From there, we can proceed as before to find x=107.
Sufficient.

I hope this helps!
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05 Oct 2010, 18:49
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TomB wrote:
x/y=5.35
If x and y are positive integers, then what is the value of x?

(1) When y is divided by x, the remainder is 20.

(2) When x is divided by y, the remainder is 7.

I surprised myself at the pace which I solved this one. Looks like a easy one.

Given x/y = 5.35 = 5 + 0.35

5 + 0.35 can be represented as 5 + 35/100 => 5 + 7/20 => 107/20

Hence x/y is 107/20.

Let us look at the statements:

1) Given y/x = some integer + 20 (remainder). We know that x/y = 107/20. Hence y/x = 20/107 -- gives us 20 as the remainder and 0 as the quotient. Sufficient.

2) Given x/y = 7. Yes this is also possible 107/20 gives us a remainder of 7. Sufficient.

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05 Oct 2010, 23:12
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TomB wrote:
x/y=5.35
If x and y are positive integers, then what is the value of x?

(1) When y is divided by x, the remainder is 20.

(2) When x is divided by y, the remainder is 7.

x/y = 5.35 = 535/100 = 107/20

x and y will be of the form 107z and 20z

(1) y is less than x so when divided by x the remainder will be y itself. So y=20. If y=20, x=107. Sufficient

(2) x divided by y leaves remainder 7.
note that 107z = 5*(20z) + 7z
and that 7z < 20z
so then the remainder is always 7z. but we know remainder is 7. so z=1
hence x=107 & y=20
Sufficient

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X/Y = 5.35 If x and y are positive integers, then what is  [#permalink]

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21 Jun 2011, 00:16
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X/Y = 5.35

If x and y are positive integers, then what is the value of x?

(1) When y is divided by x, the remainder is 20.

(2) When x is divided by y, the remainder is 7.

Master Gmat 22
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21 Jun 2011, 00:34
x = 5y + 0.35y

So remainder is 0.35y - (A)

Again,

y/x = 1/5.35 = 100/535 = 20/107 - (B)

(1)
Clearly, from (B), x = 107 as remainder is always less than divisor
Sufficient

(2)

Clearly, from (A), 0.35y = 7

So 0.05Y = 1 => y = 20

Hence X can be found as x = 5.35 * 20 = 107

Sufficient

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05 Sep 2011, 09:32
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Quote:
X/Y = 5.35

If x and y are positive integers, then what is the value of x?

(1) When y is divided by x, the remainder is 20.

(2) When x is divided by y, the remainder is 7.

Master Gmat 22

X/Y=5 + 7/20
--> Y is a multiple of 20
--> remainder is a multiple of 7

As such:
Y=20 (or multiple of 20)
remainder=7 (or multiple of 7)
--> lowest possible value of X: 5(20)+7 = 107

From Statement 1
Y/X= Integer, remainder 20
20/107 = 0 + 20
Sufficient

From Statement 2
X = multiple of Y + 7
107=5(20)+7
Sufficient

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x/y =5.35 If x and y are positive integers, then what is the  [#permalink]

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27 Oct 2011, 02:21
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x/y =5.35

If x and y are positive integers, then what is the value of x?

(1) When y is divided by x, the remainder is 20.

(2) When x is divided by y, the remainder is 7.
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28 Oct 2011, 05:20
It was confusing but I got D, and waded my way through, although not sure if correctly. This is what I did:

Simplify the given statement:

x/y = 5.35 = 5 + 35/100 = 5 + 7/20 = 107/20

So we want to verify if x = 107 and y = 20.

1) y/x has a remainder of 20. Well, flip the above statement over.
Thus, if x/y = 107/20 => y/x = 20/107

Since it is already in fractional form, the remainder is 20, we can confirm that y=20, and x=107

Sufficient.

2) x/y has a remainder of 7. We have already distilled our given statement to this (5 + 7/20). This confirms it, and thus x = 107 and y = 20.

Sufficient.

The confusing bit is in 1. It is easy to get tripped up over 20/107 and not realize that 20 is the remainder since the Quotient is 0.

You can visualize it as 20/107 = 0 + 20/107 where Quotient = 0, 20 = Remainder, and 107 = Divisor.
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Re: x/y =5.35 If x and y are positive integers, then what is the  [#permalink]

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11 Aug 2013, 22:28
Gem of a question :

hard to get the statement 1 inference , although statement 2 is easy to infer.

From above post what I can understand is that:

Since X/Y >1 => Y has to be less than X

Therefore,

When Y is divided by X then the quotient will have to be '0', since if remainder is other than '0' than Y will have a greater value than X which will contradict that X>Y as per question stem so when Y is divided by X the quotient's value should be '0' only .
Hence Y=20 so we can get the value of X using question stem

Rgds,
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Re: x/y=5.35 If x and y are positive integers, then what is the  [#permalink]

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12 Oct 2015, 12:10
Yes, let's bump it up:

x/y = 5.35

We are focusing on the remainders here, therefore let's write x/y=0.35, i.e. x=7 and y=20 or multiples thereof.

Statement 1: Exactly the reciprocal, so x = 7 and y = 20
Statement 2: Exactly what we built up above, so x = 7 and y = 20

Engr2012, is this concise?
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Re: x/y=5.35 If x and y are positive integers, then what is the  [#permalink]

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12 Oct 2015, 18:21
reto wrote:
Yes, let's bump it up:

x/y = 5.35

We are focusing on the remainders here, therefore let's write x/y=0.35, i.e. x=7 and y=20 or multiples thereof.

Statement 1: Exactly the reciprocal, so x = 7 and y = 20
Statement 2: Exactly what we built up above, so x = 7 and y = 20

Engr2012, is this concise?

x must be a multiple of 107 according to the question stem.
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Re: x/y=5.35 If x and y are positive integers, then what is the  [#permalink]

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14 Oct 2015, 03:54
1
reto wrote:
Yes, let's bump it up:

x/y = 5.35

We are focusing on the remainders here, therefore let's write x/y=0.35, i.e. x=7 and y=20 or multiples thereof.

Statement 1: Exactly the reciprocal, so x = 7 and y = 20
Statement 2: Exactly what we built up above, so x = 7 and y = 20

Engr2012, is this concise?

That is not correct reto. Although you did end up getting the correct answer, make sure to apply the concepts correctly. This is a very good example of how to interpret the divisbility formula.

When you write the divisbility formula, you get,

x=yp+r , where p is a positive integer.

Thus you get, x/y=p+r/y and this r/y=0.35 (x/y $$\neq$$.35. This is where you are making a mistake)

Per statement 2, r=7 and thus y=20, giving you x=107.

Per statement 1, y/x=q+20 , you also know that x/y=5.35 ---> x>y thus when you divide y/x (think 30/67 for example, you will geta quotient of 0 and remainder as 30, the dividend itself!!), you get 0 as the quotient and 20 as the remainder.

Thus, y must be = 20 , again giving you x = 107.

Thus both statements are sufficient individually, giving you D as the correct answer.

Hope this helps.
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Re: x/y=5.35 If x and y are positive integers, then what is the  [#permalink]

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25 Feb 2018, 23:00
x = 5.35y
x = 5y + 0.35y
x = 5y + $$\frac{7y}{20}$$

if y = 20, x = 107, remainder = 7
if y = 40, x = 214, remainder = 14
if y = 60, x = 321, remainder = 21
.
.
goes on

one thing to note, x is definitely greater than y, if it were then $$\frac{x}{y}$$ would be< 1, but $$\frac{x}{y}$$ = 5.35

Statement 1: When y is divided by x, the remainder is 20.
since x > y, y divided by x, remainder will be y itself, so it is saying y = 20, as shown above, if y = 20, x = 107 => Sufficient
Statement 2: When x is divided by y, the remainder is 7.
if remainder is 7, x = 107 as shown above => sufficient

(D)
Re: x/y=5.35 If x and y are positive integers, then what is the &nbs [#permalink] 25 Feb 2018, 23:00
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