When the positive integer x is divided by the positive integ

Question

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.

(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.

anairamitch1804 · Accepted Answer

Posting official solution of this problem.

desaichinmay22 · Answer

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

jogeshanand · Answer

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.

Bunuel · Answer

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}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.

GMATinsight · Answer

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

push12345 · Answer

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

Madhavsinghyadav · Answer

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?

Bunuel · Answer

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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When the positive integer x is divided by the positive integ

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When the positive integer x is divided by the positive integ

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