January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2447

If X is an integer, does 7X + 9X+3 end with a 0?
[#permalink]
Show Tags
Updated on: 13 Aug 2018, 01:36
Question Stats:
80% (01:26) correct 20% (01:53) wrong based on 203 sessions
HideShow timer Statistics
eGMAT Question: If \(X\) is an integer, does \(7^X + 9^{X+3}\) end with a 0? 1) \(2^X\) is odd 2) (\(2X+2\)) is even A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statements (1) and (2) TOGETHER are NOT sufficient. This is Question 2 of The eGMAT Number Properties Marathon Go to Question 3 of the Marathon
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82

Re: If X is an integer, does 7X + 9X+3 end with a 0?
[#permalink]
Show Tags
27 Feb 2018, 09:39
EgmatQuantExpert wrote: Question: If \(X\) is an integer, does \(7^X + 9^{X+3}\) end with a 0? 1) \(2^X\) is odd 2) (\(2X+2\)) is even A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statements (1) and (2) TOGETHER are NOT sufficient. We need the value of \(x\) to determine the unit's digit Statement 1: \(2^x\) is odd implies \(x=0\) because \(2^0=1\), for any other value of \(x\), \(2^x\) will be either an even number or a non integer. SufficientStatement 2: \(2x+2=even => x\) is either even or odd but we cannot determine the value of \(x\) from this. InsufficientOption A



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2447

If X is an integer, does 7X + 9X+3 end with a 0?
[#permalink]
Show Tags
Updated on: 04 Nov 2018, 02:19
Solution: The units digit of the expression \(7^X + 9^{X+3}\) will end with a zero, only when \(X\) is of the form \(4k\), i.e., a multiple of \(4\). Step 1: Analyse Statement 1:\(2^X\) is odd. • As per our conceptual knowledge, any even number when raised to a power will result in an even number only. • However, this is not always true.
o Consider the example when an even number is raised to the power 0. o It has been taught in our concept file that any number (except 0) when raised to the power 0, will yield 1 as the answer. So, for 2X to be odd, X should be equal to 0.
Since 0 can be written in the form of 4k, where k =0, Statement 1 alone is sufficient to answer the question. Step 2: Analyse Statement 2:\((2X+2)\) is Even. • \(2X\) is always even irrespective of the evenodd nature of \(X\).
o This is because \(X\) is multiplied by an even number (2), and from our conceptual knowledge we know that, o Even * Even = Even o Even * Odd = Even • \(2\) is an even number • Therefore, from this statement, the evenodd nature of X cannot be determined. Since we do not know the exact evenodd nature of X, Statement 2 alone is NOT sufficient to answer the question. Hence, we can eliminate answer choice B. Step 3: Combine both Statements:This step is not required since we already got a unique answer in step 3. Correct Answer: Option A
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Intern
Joined: 09 Jun 2018
Posts: 8

Re: If X is an integer, does 7X + 9X+3 end with a 0?
[#permalink]
Show Tags
03 Nov 2018, 03:36
EgmatQuantExpert wrote: Solution: The units digit of the expression \(7^X + 9^{X+3}\) will end with a zero, only when \(X\) is of the form \(4k\), i.e., a multiple of \(4\). Step 1: Analyse Statement 1:\(2^X\) is odd. • As per our conceptual knowledge, any even number when raised to a power will result in an even number only. • However, this is not always true.
o Consider the example when an even number is raised to the power 0. o It has been taught in our concept file that any number (except 0) when raised to the power 0, will yield 1 as the answer. So, for 2X to be odd, X should be equal to 0.
Since 0 can be written in the form of 4k, where k =0, Statement 1 alone is sufficient to answer the question. Step 2: Analyse Statement 2:\((2X+2)\) is Even. • \(2X\) is always even irrespective of the evenodd nature of \(X\).
o This is because \(X\) is multiplied by an even number (2), and from our conceptual knowledge we know that, o Even * Even = Even o Even * Odd = Even • \(2\) is an even number • Therefore, from this statement, the evenodd nature of X cannot be determined. Since we do not know the exact evenodd nature of X, Statement 2 alone is NOT sufficient to answer the question. Hence, we can eliminate answer choice B. Step 3: Combine both Statements:This step is not required since we already got a unique answer in step 3. Correct Answer: Option C Dear Payal, perfect explanation, thanks. Just a typo in your writeup, correct answer is A, not C



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2447

Re: If X is an integer, does 7X + 9X+3 end with a 0?
[#permalink]
Show Tags
04 Nov 2018, 02:20



Intern
Joined: 04 Aug 2018
Posts: 7

Re: If X is an integer, does 7X + 9X+3 end with a 0?
[#permalink]
Show Tags
04 Nov 2018, 15:56
EgmatQuantExpert wrote: Solution: The units digit of the expression \(7^X + 9^{X+3}\) will end with a zero, only when \(X\) is of the form \(4k\), i.e., a multiple of \(4\). Step 1: Analyse Statement 1:\(2^X\) is odd. • As per our conceptual knowledge, any even number when raised to a power will result in an even number only. • However, this is not always true.
o Consider the example when an even number is raised to the power 0. o It has been taught in our concept file that any number (except 0) when raised to the power 0, will yield 1 as the answer. So, for 2X to be odd, X should be equal to 0.
Since 0 can be written in the form of 4k, where k =0, Statement 1 alone is sufficient to answer the question. Step 2: Analyse Statement 2:\((2X+2)\) is Even. • \(2X\) is always even irrespective of the evenodd nature of \(X\).
o This is because \(X\) is multiplied by an even number (2), and from our conceptual knowledge we know that, o Even * Even = Even o Even * Odd = Even • \(2\) is an even number • Therefore, from this statement, the evenodd nature of X cannot be determined. Since we do not know the exact evenodd nature of X, Statement 2 alone is NOT sufficient to answer the question. Hence, we can eliminate answer choice B. Step 3: Combine both Statements:This step is not required since we already got a unique answer in step 3. Correct Answer: Option A Dear Payal , thanks for your answer but i do not know why the units digit of the expression 7X+9X+3 7 X + 9 X + 3 will end with a zero, only when X X is of the form 4k 4 k , i.e., a multiple of 4 4.




Re: If X is an integer, does 7X + 9X+3 end with a 0? &nbs
[#permalink]
04 Nov 2018, 15:56






