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03 Sep 2018, 01:50
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D
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Difficulty:
35%
(medium)
Question Stats:
63% (01:16) correct
37%
(01:11)
wrong
based on 30
sessions
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If \(x\) is a positive integer, which of the following is not necessarily a divisor of \(x(x + 1)(x + 2)\)?
A. \(x\)
B. 2
C. 3
D. 4
E. 6
A. \(x\)
B. 2
C. 3
D. 4
E. 6
03 Sep 2018, 01:50
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Official Solution:
If \(x\) is a positive integer, which of the following is not necessarily a divisor of \(x(x + 1)(x + 2)\)?
A. \(x\)
B. 2
C. 3
D. 4
E. 6
We’ll go for ALTERNATIVE since we’re asked about an expression with variables.
When looking at the answers, \(x\) is definitely a divisor, since it is a multiplier in the expression itself. But what about the rest of the answers? Since this is an expression with only letters, we can pick a number: \(x = 1\) gives us \(1 × 2 × 3 = 6\). So 2, 3, and 6 are all divisors of 6, but 4 isn’t.
Answer: D
If \(x\) is a positive integer, which of the following is not necessarily a divisor of \(x(x + 1)(x + 2)\)?
A. \(x\)
B. 2
C. 3
D. 4
E. 6
We’ll go for ALTERNATIVE since we’re asked about an expression with variables.
When looking at the answers, \(x\) is definitely a divisor, since it is a multiplier in the expression itself. But what about the rest of the answers? Since this is an expression with only letters, we can pick a number: \(x = 1\) gives us \(1 × 2 × 3 = 6\). So 2, 3, and 6 are all divisors of 6, but 4 isn’t.
Answer: D
15 Sep 2018, 21:19
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I don't understand this question. If we are allowed to "pick a number" and I choose x=4 then the solution is divisible by all the answer choices. I must try another number that isn't divisible by all the answers?
x=1
1(1+1)(1+2)
(1)(2)(3)= 6 (which is not divisible by 4
but what if I choose x=4
4(4+1)(4+2)
4(5)(6)= 120 (divisible by 3,6,and 4.
Do I have to chose a number that is not a possible answer?
x=1
1(1+1)(1+2)
(1)(2)(3)= 6 (which is not divisible by 4
but what if I choose x=4
4(4+1)(4+2)
4(5)(6)= 120 (divisible by 3,6,and 4.
Do I have to chose a number that is not a possible answer?
