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If n is an integer, is n even? [#permalink]
 26 Aug 2012, 03:12
Question Stats:
81% (01:42) correct
18% (00:33) wrong based on 2 sessions
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectIf n is an integer, is n even? (1) n^2 - 1 is an odd integer. (2) 3n + 4 is an even integer. Practice Questions
Question: 27
Page: 277
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Re: If n is an integer, is n even? [#permalink]
26 Aug 2012, 03:13
SOLUTION:If n is an integer, is n even?(1) n^2 - 1 is an odd integer --> n^2-1=odd --> n^2=odd+1=even. Now, since n is an integer, then in order n^2 to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some irrational number (square root of an even number), for example \sqrt{2}, so not an even integer.(2) 3n + 4 is an even integer --> 3n + 4=even --> 3n=even-4=even. The same here, since n is an integer, then in order 3n to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some fraction, for example \frac{2}{3}, so not an even integer.Answer: D.
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Re: If n is an integer, is n even? [#permalink]
27 Aug 2012, 09:07
If n is an integer, is n even?
(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.
If n^2 - 1 is odd ,then n^2 is even.Assuming both Positive and Negative integers fall under even category,I ca say n is even.
So statement 1 is alone sufficient.
If 3n + 4 is an even integer,then 3n is also even. Since 3 is odd, n has to be even.
So statement 2 is also sufficient.
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Re: If n is an integer, is n even? [#permalink]
30 Aug 2012, 03:50
answer D. both statements are individually sufficient
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Re: If n is an integer, is n even? [#permalink]
30 Aug 2012, 11:32
(1) n^2 - 1 is odd. The next consecutive integer is n^2 and is therefore even. This means that n must be even too, because squaring a number does NOT change this. --> sufficient
(2) 3n + 4 is even. So 3n is even, too. This means that the prime factorization of 3n includes at least one 2. Dividing by 3 (to get from 3n to n) does NOT eliminate recude the number of twos in the prime factorization, so n is even. --> sufficient
The correct answer is D. Both statements are individually sufficient.
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Re: If n is an integer, is n even? [#permalink]
30 Aug 2012, 19:56
i will go with d both options individually can get the required info -as its an integer no more fractions integer when squared gives the same type value i.e odd gives odd and even gives even same way multiplying odd with even gives even and odd with odd gives odd hence both are individually sufficient
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Re: If n is an integer, is n even? [#permalink]
31 Aug 2012, 02:33
SOLUTION:If n is an integer, is n even?(1) n^2 - 1 is an odd integer --> n^2-1=odd --> n^2=odd+1=even. Now, since n is an integer, then in order n^2 to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some irrational number (square root of an even number), for example \sqrt{2}, so not an even integer.(2) 3n + 4 is an even integer --> 3n + 4=even --> 3n=even-4=even. The same here, since n is an integer, then in order 3n to be even n must be even. Sufficient. Notice that if we were not told that n is an integer, then n could be some fraction, for example \frac{2}{3}, so not an even integer.Answer: D.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
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Re: If n is an integer, is n even?
[#permalink]
31 Aug 2012, 02:33
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