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505-555 Level|   Algebra|   Inequalities|      
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What is the value of positive integer x? (1) 1 ≤ x^5 ≤ 36 (2) 2x ≠ x^2 18 Mar 2021, 01:30
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C
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Question Stats:

80% (01:14) correct 20% (01:26) wrong based on 128 sessions

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What is the value of positive integer x?

(1) 1 ≤ x^5 ≤ 36
(2) 2x ≠ x^2


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What is the value of positive integer x? (1) 1 ≤ x^5 ≤ 36 (2) 2x ≠ x^2 19 Mar 2021, 01:15
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Bunuel
What is the value of positive integer x?

(1) 1 ≤ x^5 ≤ 36
(2) 2x ≠ x^2


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What is the value of positive integer x?

(1) 1 ≤ x^5 ≤ 36. Since x is a positive integer, then x can be 1 or 2. Not sufficient.

(2) 2x ≠ x^2 --> \(x^2-2x\neq{0}\) --> \(x(x-2)\neq{0}\) --> \(x\neq{0}\) and \(x\neq{2}\). Not sufficient.

(1)+(2) Since from (2) x is not 2, then from (1) x must be 1. Sufficient.

Answer: C.

Hope it's clear.
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What is the value of positive integer x? (1) 1 ≤ x^5 ≤ 36 (2) 2x ≠ x^2 18 Mar 2021, 02:16
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Bunuel
What is the value of positive integer x?

(1) 1 ≤ x^5 ≤ 36
(2) 2x ≠ x^2

Question: Integer x = ?

Statement 1: 1 ≤ x^5 ≤ 36
Because
\(1^5 = 1\)
\(2^5 = 32\) and both satisfy the inequation of statement 1

therefore, x may be either 1 or 2 hence

NOT SUFFICIENT

Statement 2: \(2x ≠ x^2\)

i.e. x ≠ 2 but x may be any positive integer other than 2 hence

NOT SUFFICIENT

COmbining the statements

x = 1 as x ≠2 hence

SUFFICIENT

Answer: Option C
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What is the value of positive integer x? (1) 1 ≤ x^5 ≤ 36 (2) 2x ≠ x^2 18 Mar 2021, 05:18
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Statement 1 : 1) 1 ≤ x^5 ≤ 36

Possible values for X

1^5 = 1 .... Valid
2^5 = 32 .... Valid
3^5 = 243 .... Invalid

Possible values : 1 or 2

Insufficient.


Statement 2 : (2) 2x ≠ x^2

So x ≠ 2 but we still don't know what is the value of x.

Insufficient.

Combining two statements

From Statement 1: X can be 1 or 2
From Statement 2: X is not 2 for sure.
Hence, x has to be equal to 1.

Sufficient. Answer choice (C)
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What is the value of positive integer x? (1) 1 ≤ x^5 ≤ 36 (2) 2x ≠ x^2 18 Mar 2021, 22:20
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What is the value of positive integer x?

(1) 1 ≤ x^5 ≤ 36
x can be 1 or 2
Not sufficient

(2) 2x ≠ x^2
x can be any integer except 0 or 2
Not sufficient

(1) + (2)
x = 1

Sufficient

Option C

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What is the value of positive integer x? (1) 1 ≤ x^5 ≤ 36 (2) 2x ≠ x^2 18 Mar 2021, 22:56
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What is the value of positive integer x?

Stat1: 1 ≤ x^5 ≤ 36
x = 1 or 2. Not sufficient.

Stat2: 2x ≠ x^2
or, x*(x-2) ≠ 0 or, x ≠ 0 or 2 Not sufficient.

Combining both, x = 1, as x ≠2. I think C. :)
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What is the value of positive integer x? (1) 1 ≤ x^5 ≤ 36 (2) 2x ≠ x^2 11 Feb 2023, 11:21
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