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Which of the following CANNOT yield an integer when divided

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Which of the following CANNOT yield an integer when divided [#permalink] New post 21 Feb 2014, 00:08
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Which of the following CANNOT yield an integer when divided by 10 ?

(A) The sum of two odd integers
(B) An integer less than 10
(C) The product of two primes
(D) The sum of three consecutive integers
(E) An odd integer

Problem Solving
Question: 109
Category: Arithmetic Operations on rational numbers
Page: 75
Difficulty: 600


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Re: Which of the following CANNOT yield an integer when divided [#permalink] New post 21 Feb 2014, 00:08
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SOLUTION

Which of the following CANNOT yield an integer when divided by 10 ?

(A) The sum of two odd integers
(B) An integer less than 10
(C) The product of two primes
(D) The sum of three consecutive integers
(E) An odd integer

In order an integer to be divisible by 10=2*5, the integer must be divisible by 2 (and 5), so it must be even, thus an odd integer is never divisible by 10 (or another way, an integer to be divisible by 10 its units digit must be 0, thus it must be even).

To discard other options:
(A) The sum of two odd integers. Not true: for example, 5+5=10 --> 10 IS divisible by 10.
(B) An integer less than 10. Not true: for example 0 IS divisible by 10.
(C) The product of two primes. Not true: 2*5=10 --> 10 IS divisible by 10.
(D) The sum of three consecutive integers. Not true: for example, -1+0+1=0 --> 0 IS divisible by 10.

Answer: E.
_________________

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: Which of the following CANNOT yield an integer when divided [#permalink] New post 21 Feb 2014, 02:00
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IMO (E)
A) The sum of two odd integers - It could or could not yield integer: 3+5=8 or 25+5=30
B) An integer less than 10 - It could or could not yield integer: 3 or -30
C) The product of two primes -It could or could not yield integer: 2*3=6 or 5*2=10
D) The sum of three consecutive integers -It could or could not yield integer: 2+3+4=9 or 9+10+11=30
(E) An odd integer - it can't yield integer when divided by 10: Number should contain at least one 2 and 5 to yield an integer.
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Re: Which of the following CANNOT yield an integer when divided [#permalink] New post 22 Feb 2014, 00:22
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We can test examples as below:

A) 15+5 is divisible by 10
B) -10 is divisble by 10
C) 2*5 is divisible by 10
D) (19+20+21) is divisible by 10
E) All odd integers are not divisible by 10

Answer E.
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Re: Which of the following CANNOT yield an integer when divided [#permalink] New post 22 Feb 2014, 05:32
Expert's post
SOLUTION

Which of the following CANNOT yield an integer when divided by 10 ?

(A) The sum of two odd integers
(B) An integer less than 10
(C) The product of two primes
(D) The sum of three consecutive integers
(E) An odd integer

In order an integer to be divisible by 10=2*5, the integer must be divisible by 2 (and 5), so it must be even, thus an odd integer is never divisible by 10 (or another way, an integer to be divisible by 10 its units digit must be 0, thus it must be even).

To discard other options:
(A) The sum of two odd integers. Not true: for example, 5+5=10 --> 10 IS divisible by 10.
(B) An integer less than 10. Not true: for example 0 IS divisible by 10.
(C) The product of two primes. Not true: 2*5=10 --> 10 IS divisible by 10.
(D) The sum of three consecutive integers. Not true: for example, -1+0+1=0 --> 0 IS divisible by 10.

Answer: E.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Which of the following CANNOT yield an integer when divided   [#permalink] 22 Feb 2014, 05:32
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