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EgmatQuantExpert

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
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Dear Payal,

perfect explanation, thanks. Just a typo in your write-up, correct answer is A, not C

Hey MarcoAD,
Thanks for pointing out the typo. We have rectified it. :)
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EgmatQuantExpert

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

.
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