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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 [#permalink]

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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.
[Reveal] Spoiler: OA
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Re: When the positive integer x is divided by the positive integ [#permalink]

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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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When the positive integer x is divided by the positive integ [#permalink]

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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: When the positive integer x is divided by the positive integ [#permalink]

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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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Re: When the positive integer x is divided by the positive integ [#permalink]

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Is z>b ? [#permalink]

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New post 15 Apr 2018, 04:46
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.
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Re: Is z>b ? [#permalink]

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New post 15 Apr 2018, 05:16
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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Is z>b ? [#permalink]

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New post 15 Apr 2018, 07:57
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GMATinsight wrote:
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


Dear GMATinsight

While I have arrived to same conclusion for statement 1 as you did, I have arrived to different conclusion for statement 2.

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

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

We are dealing with POSITIVE integers.....so 3a > 2a & 3y > 2y
But we have 2a > 3y Therefore:

3a > 2a > 3y > 2y......3a > 2y...same as statement 1...........Sufficient

Another way to plug positive integer numbers:

Let a =2 & y = 1.........2 (2) > 3(1)...... 2y + z = 3a + b..........2+z = 6+b.............z-b = 4...z must be greater than b

Let a =3 & y = 1.........2 (3) > 3(1)...... 2y + z = 3a + b..........2+z = 9+b.............z-b = 7...z must be greater than b

Let a =7 & y = 6.........2 (7) > 3(6)...... 2y + z = 3a + b..........12+z = 21+b.............z-b = 8...z must be greater than b

Sufficient

Where did I wrong in my solution?

Thanks
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Re: When the positive integer x is divided by the positive integ [#permalink]

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New post 15 Apr 2018, 09:21
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.


Please follow the rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html Pay attention to rules 1 and 3. Thank you.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: When the positive integer x is divided by the positive integ [#permalink]

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New post 15 Apr 2018, 11:03
Mo2men wrote:
GMATinsight wrote:
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


Dear GMATinsight

While I have arrived to same conclusion for statement 1 as you did, I have arrived to different conclusion for statement 2.

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

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


We are dealing with POSITIVE integers.....so 3a > 2a & 3y > 2y
But we have 2a > 3y Therefore:

3a > 2a > 3y > 2y......3a > 2y...same as statement 1...........Sufficient

Another way to plug positive integer numbers:

Let a =2 & y = 1.........2 (2) > 3(1)...... 2y + z = 3a + b..........2+z = 6+b.............z-b = 4...z must be greater than b

Let a =3 & y = 1.........2 (3) > 3(1)...... 2y + z = 3a + b..........2+z = 9+b.............z-b = 7...z must be greater than b

Let a =7 & y = 6.........2 (7) > 3(6)...... 2y + z = 3a + b..........12+z = 21+b.............z-b = 8...z must be greater than b

Sufficient

Where did I wrong in my solution?

Thanks


Hello

Please check the highlighted part.
y/a > 2/3 means 3y > 2a. I think by mistake you have written it as 3y < 2a
Re: When the positive integer x is divided by the positive integ   [#permalink] 15 Apr 2018, 11:03
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