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21 Dec 2023, 07:00
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D
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Difficulty:
95%
(hard)
Question Stats:
40% (02:13) correct
60%
(02:04)
wrong
based on 167
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
If © denotes one of three arithmetic operations, addition, subtraction, or division, and if x is a positive integer, what is the value of x?
(1) 1©x = x
(2) 2©x > x©2
If © denotes one of three arithmetic operations, addition, subtraction, or division, and if x is a positive integer, what is the value of x?
(1) 1©x = x
(2) 2©x > x©2
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22 Dec 2023, 06:17
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GMAT Club Official Explanation:
If © denotes one of three arithmetic operations, addition, subtraction, or division, and if x is a positive integer, what is the value of x?
(1) 1©x = x
If © represents addition, we'd have 1 + x = x, which cannot be true for any value of x. Hence, © is not addition.
If © represents subtraction, we'd have 1 - x = x, which simplifies to x = 1/2. However, since x must be a positive integer, © cannot be subtraction.
Therefore, © must represent division. In this case, 1/x = x, leading to x^2 = 1. Since x is a positive integer, x must be 1.
Sufficient.
(2) 2©x > x©2
If © represents addition, we'd have 2 + x > x + 2, which is not true for any value of x. Hence, © is not addition.
If © represents subtraction, we'd have 2 - x > x - 2, simplifying to x < 2. Given that x is a positive integer, if © is subtraction, then x must be 1.
If © represents division, we'd have 2/x > x/2. Cross-multiplying (we can safely do that since x is a positive integer) gives x^2 < 4, which narrows down to -2 < x < 2. As x is a positive integer, x must be 1. Therefore, if © is division, x is 1.
In both viable cases (subtraction or division), x turns out to be 1.
Sufficient.
Answer: D
General Discussion
27 Mar 2025, 11:33
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For the first statement, why can't 1 C x = x
here C can be multiplication as well...
1 * any number = number
So there are 2 operations x, / for first statement, not sufficient.
here C can be multiplication as well...
1 * any number = number
So there are 2 operations x, / for first statement, not sufficient.
