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Updated on: 13 Aug 2018, 02:36
Originally posted by EgmatQuantExpert on 27 Feb 2018, 10:04.
Last edited by EgmatQuantExpert on 13 Aug 2018, 02:36, edited 2 times in total.
Last edited by EgmatQuantExpert on 13 Aug 2018, 02:36, edited 2 times in total.
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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78% (01:46) correct
22%
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e-GMAT 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 e-GMAT Number Properties Marathon
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27 Feb 2018, 10:39
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EgmatQuantExpert
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
Option A
Updated on: 04 Nov 2018, 03:19
Originally posted by EgmatQuantExpert on 27 Feb 2018, 23:22.
Last edited by EgmatQuantExpert on 04 Nov 2018, 03:19, edited 1 time in total.
Last edited by EgmatQuantExpert on 04 Nov 2018, 03:19, edited 1 time in total.
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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.
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
• 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
