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a, b, c, and d are positive integers. If the remainder is 9

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a, b, c, and d are positive integers. If the remainder is 9 [#permalink] New post 07 Jan 2013, 05:59
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a, b, c, and d are positive integers. If the remainder is 9 when a is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?

(A) 20
(B) 19
(C) 18
(D) 16
(E) 15
[Reveal] Spoiler: OA

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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink] New post 07 Jan 2013, 06:21
When a is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.
b + d cannot be 15, hence E is the answer.
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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink] New post 09 Jan 2013, 15:12
a/b gives reminder 9, hence b\geq{10}
c/d gives reminder 5, hence d\geq{6}

Add above inequalities:
(b+d)\geq{16}

Among the answer choices, the only value that does NOT satisfy above constraint is 15.

Hence choice(E) is the answer.
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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink] New post 10 Jan 2013, 03:15
PraPon wrote:
a/b gives reminder 9, hence b\geq{10}
c/d gives reminder 5, hence d\geq{6}[/
m]

Add above inequalities:
[m](b+d)\geq{16}


Among the answer choices, the only value that does NOT satisfy above constraint is 15.

Hence choice(E) is the answer.


Hi can u please explain highlighted part? I missing sumthing here..
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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink] New post 10 Jan 2013, 03:31
Expert's post
bhavinshah5685 wrote:
PraPon wrote:
a/b gives reminder 9, hence b\geq{10}
c/d gives reminder 5, hence d\geq{6}[/
m]

Add above inequalities:
[m](b+d)\geq{16}


Among the answer choices, the only value that does NOT satisfy above constraint is 15.

Hence choice(E) is the answer.


Hi can u please explain highlighted part? I missing sumthing here..


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.

For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since 15 = 6*2 + 3.

Notice that 0\leq{r}<x means that remainder is a non-negative integer and always less than divisor.

For more check Remainders chapter of Math Book: remainders-144665.html

a, b, c, and d are positive integers. If the remainder is 9 when a is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?

(A) 20
(B) 19
(C) 18
(D) 16
(E) 15

According to the above, since the remainder is 9 when a is divided by b, then b (divisor) must be greater than 9 (remainder). So, the least value of b is 10.

Similarly, since he remainder is 5 when c is divided by d, then d must be greater than 5. So, the least value of d is 6.

Hence, the least value of b + d is 10 + 6 = 16. Therefore 15 (option E) is NOT a possible value for b + d.

Answer: E.

Hope it's clear.
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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink] New post 06 Apr 2014, 09:27
what if a = 1 and b= 9...then wouldn't 1/9 still have a remainder of 9? doesn't the rule that b must be greater than or equal to 10 not hold in this case?


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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink] New post 06 Apr 2014, 09:39
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HCalum11 wrote:
what if a = 1 and b= 9...then wouldn't 1/9 still have a remainder of 9? doesn't the rule that b must be greater than or equal to 10 not hold in this case?


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No.

Let me ask you a question: how many leftover apples would you have if you had 1 apple and wanted to distribute in 9 baskets evenly? Each basket would get 0 apples and 1 apple would be leftover (remainder).

When a divisor is more than dividend, then the remainder equals to the dividend, for example:
3 divided by 4 yields the reminder of 3: 3=4*0+3;
9 divided by 14 yields the reminder of 9: 9=14*0+9;
1 divided by 9 yields the reminder of 1: 1=9*0+1.

Theory on remainders problems: remainders-144665.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

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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: a, b, c, and d are positive integers. If the remainder is 9   [#permalink] 06 Apr 2014, 09:39
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