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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.
(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.
Posting official solution of this problem.
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chetan86
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
General Discussion
Posts: 7
Updated on: 09 Jul 2014, 20:45
Originally posted by jogeshanand on 09 Jul 2014, 09:23.
Last edited by jogeshanand on 09 Jul 2014, 20:45, edited 1 time in total.
Last edited by jogeshanand on 09 Jul 2014, 20:45, edited 1 time in total.
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.
Please shed some light on this.
jogeshanand
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
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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selim
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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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
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
Posts: 5
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?
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?
Madhavsinghyadav
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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