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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

When the positive integer x is divided by the positive integ

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

When the positive integer x is divided by the positive integ

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards