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When the positive integer x is divided by the positive integ

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chetan86
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When the positive integer x is divided by the positive integ [#permalink] New post   09 Jul 2014, 08:01
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When the positive integer x is divided by the positive integer y, the quotient is 2 and the remainder is z. When x is divided by the positive integer a, the quotient is 3 and the remainder is b. Is z > b?

(1) The ratio of y to a is less than 3 to 2.
(2) The ratio of y to a is greater than 2 to 3.
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desaichinmay22
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Re: When the positive integer x is divided by the positive integ [#permalink] New post   09 Jul 2014, 08:39
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chetan86 wrote:
When the positive integer x is divided by the positive integer y, the quotient is 2 and the remainder is z. When x is divided by the positive integer a, the quotient is 3 and the remainder is b. Is z > b?

(1) The ratio of y to a is less than 3 to 2.
(2) The ratio of y to a is greater than 2 to 3.



Given :
x=2y+z
x=3a+b

Therefor, 2y+z=3a+b

Statement 1:
y/a<3/2
2y<3a

since,2y+z=3a+b and 2y<3a, z>b for equality to hold true.
sufficient statement

Statement 2:
y/a>2/3
3y>2a

Statement is insufficient to comment whether z>b.

Ans=A
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Re: When the positive integer x is divided by the positive integ [#permalink] New post   07 Mar 2017, 13:53
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Posting official solution of this problem.
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Re: When the positive integer x is divided by the positive integ [#permalink] New post   09 Jul 2014, 10:36
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jogeshanand wrote:
Curious to know whether z and b can be negative. In general, do we have to consider the case for negative remainders as well in such questions
Please shed some light on this.


No, at least on the GMAT.

OG12:
If \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).

Theory on remainders problems: remainders-144665.html
Tips: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1376126

Units digits, exponents, remainders problems: new-units-digits-exponents-remainders-problems-168569.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199


Hope this helps.
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When the positive integer x is divided by the positive integ [#permalink] New post   Updated on: 09 Jul 2014, 21:45
Curious to know whether z or b can be negative. In general, do we have to consider the case for negative remainders as well in such questions
Please shed some light on this.

Originally posted by jogeshanand on 09 Jul 2014, 10:23.
Last edited by jogeshanand on 09 Jul 2014, 21:45, edited 1 time in total.
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Re: Is z>b ? [#permalink] New post   15 Apr 2018, 05:16
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selim wrote:
When the positive integer x is divided by the positive integer y the quotient is 2 and the remainder is z. when x is divided by the positive integer a the quotient is 3 and the remainder is b. Is z>b ?

1)the ration of y to a is less than 3 to 2.
2)the ratio of y to a is greater than 2 to 3.


When the positive integer x is divided by the positive integer y the quotient is 2 and the remainder is z

i.e. x = 2y + z

when x is divided by the positive integer a the quotient is 3 and the remainder is b

i.e. x = 3a + b

i.e. 2y + z = 3a + b

Question : Is z > b ?
Or
Question : Is 2y > 3a ?

Statement 1: the ratio of y to a is less than 3 to 2.

i.e. y / a < 3/2
i.e. 2y < 3a
SUFFICIENT

Statement 2: the ratio of y to a is greater than 2 to 3

i.e. y / a > 2/3
i.e. 3y < 2a
NOT SUFFICIENT

Answer: Option A
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Re: When the positive integer x is divided by the positive integ [#permalink] New post   29 Apr 2018, 02:11
As per question

X=2y+z
X=3a+b

2y+z=3a+b

I)y/a<1.5
3a>2y so in order to maintain equality
Z>b sufficient

II)y/a>0.6
3a can be > or < 2y
So can't say about z or b

A is answer

Posted from my mobile device
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Re: When the positive integer x is divided by the positive integ [#permalink] New post   02 Mar 2024, 13:25
Bunuel
i approached second statement as if y/a is greater than 2/3 which is equivalent to 0.66 , so i chose 3/4 which is greater than 2/3 as the statement states then putting the value in equation i finally got z=6+b which shows that z is greater than b. kindly,tell me what is wrong in this approach?
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Re: When the positive integer x is divided by the positive integ [#permalink] New post   02 Mar 2024, 16:24
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Madhavsinghyadav wrote:
Bunuel

When the positive integer x is divided by the positive integer y, the quotient is 2 and the remainder is z. When x is divided by the positive integer a, the quotient is 3 and the remainder is b. Is z > b?

(1) The ratio of y to a is less than 3 to 2.
(2) The ratio of y to a is greater than 2 to 3.

i approached second statement as if y/a is greater than 2/3 which is equivalent to 0.66 , so i chose 3/4 which is greater than 2/3 as the statement states then putting the value in equation i finally got z=6+b which shows that z is greater than b. kindly,tell me what is wrong in this approach?

­­
Why should y/a > 2/3 mean that y/a is necessarily 3/4? Please review solution HERE. It's quite clear.
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Re: When the positive integer x is divided by the positive integ [#permalink]
02 Mar 2024, 16:24
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