Is c^(abcd) = 1? (1) |a|>|b|>|c|>|d|​ (2) c^d>3 GMAT Data Sufficiency

Question - Is c^abcd=1?

1. |a|>|b|>|c|>|d|
2. c^d>3

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.        
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.        
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.        
4. EACH statement ALONE is sufficient.        
5. Statements (1) and (2) TOGETHER are not sufficient.

‘Is c^abcd=1? (1) |a|>|b|>|c|>|d|​ (2) c^d>3’- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

There is only one approach to solving the problem statement

We need to find if c^abcd=1 or not

Now,let us do some pre-analysis before analyzing each statement.
If c = 1, then c^abcd will be 1
If c = -1 and {abcd} is even, then also we’ll get c^abcd=1
If abcd = 0 and c ≠ 0, then even in that case c^abcd=1
Keeping the above in mind, let’s look at the first statement.

Statement 1: |a|>|b|>|c|>|d|
From this statement, we can infer that magnitude wise, a, b, c, and d are all distinct.
And since all modulus value is positive or 0, we can be sure that c ≠ 0, since |c| > |d|
Now, let’s take two scenarios:

Case 1: d =0
We get: c^abcd=c^0=1

Case 2: d ≠ 0
Then c^abcd may or may not be equal to 1. Thus, statement 1 is not sufficient to answer the question.

Statement 2: c^d>3

• This statement, clearly tell us that c ≠ 1 or -1
• Also, d ≠ 0

However, we don’t know any about a and b, if any one turns out to be 0, then
c^abcd could turn out to be 1.
Thus, statement 2 is also not sufficient to answer the question.
Combining both statements:

• |a| > |b| > |c| > |d|
• d ≠ 0 and c ≠ 1 or -1

If d ≠ 0, then that means a, b, or c are also not equal to 0. Thus, abcd ≠ 0
Also, since c ≠ 1 or – 1, this helps us infer that
c^abcd ≠1
This helps us to find out if c^abcd ≠1 or c^abcd =1
Since, c^abcd ≠1, thus, the correct answer is Option C.

Correct Answer: C

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