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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.
Re: If X is an integer, does 7X + 9X+3 end with a 0?
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27 Feb 2018, 10:39
1
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. Sufficient
Statement 2: \(2x+2=even => x\) is either even or odd but we cannot determine the value of \(x\) from this. Insufficient
If X is an integer, does 7X + 9X+3 end with a 0?
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Updated on: 04 Nov 2018, 03:19
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 even-odd 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 even-odd nature of X cannot be determined.
Since we do not know the exact even-odd 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
_________________
Re: If X is an integer, does 7X + 9X+3 end with a 0?
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03 Nov 2018, 04:36
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 even-odd 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 even-odd nature of X cannot be determined.
Since we do not know the exact even-odd 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 write-up, correct answer is A, not C
Re: If X is an integer, does 7X + 9X+3 end with a 0?
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04 Nov 2018, 16:56
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 even-odd 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 even-odd nature of X cannot be determined.
Since we do not know the exact even-odd 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 .
gmatclubot
Re: If X is an integer, does 7X + 9X+3 end with a 0?
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04 Nov 2018, 16:56
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80% (01:48) correct 
