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E
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Difficulty:
75%
(hard)
Question Stats:
43% (01:36) correct
57%
(01:19)
wrong
based on 97
sessions
History
Date
Time
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Not Attempted Yet
If X is a 3-digit number, is it odd?
(1) X is a perfect square.
(2) X is a palindrome.
(1) X is a perfect square.
(2) X is a palindrome.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
aa008
OA: E
1). X is a perfect square.
X can be \(121,144,169...\) and so on.
Unit digit of X can be even or odd
Statement 1 alone is not sufficient.
2). X is a palindrome.
X can be \(121,131,141,.....212,222\) and so on.
Unit digit of X can be even or odd
Statement 2 alone is not sufficient.
Combining \((1)\) and \((2)\),X should be a perfect square and a palindrome.
X can be \(121(11^2), 484(22^2)\) as there is no unique value of X and unit digit of X can be even or odd, Combining (1) and (2) will also be insufficient.
23 Sep 2018, 01:35
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Solution
Given:
- • X is a 3-digit number
To find:
- • Whether X is odd or not.
Analysing Statement 1
As per the information given in statement 1, X is a perfect square.
- • Starting from 100 to 961, we have many even and odd perfect squares
Therefore, statement 1 is not sufficient
Analysing Statement 2
As per the information given in statement 2, X is palindrome.
- • In 3-digits, we have many even as well as odd numbers which are palindromes.
Therefore, statement 2 is not sufficient.
Combining Both Statements
We know, X is a 3-digit perfect square, which is also a palindrome.
Possible values of X can be
- • \(11^2 = 121\)
• \(22^2 = 484\)
• \(26^2 = 676\)
As we can see, X can be both even or odd.
Hence, the correct answer is option E.
