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Nomayer28
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If x is a product of 4 consecutive integers, and x is divisible by 11 07 Nov 2024, 00:13
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E
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64% (01:44) correct 36% (01:58) wrong based on 200 sessions

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If x is a product of 4 consecutive integers, and x is divisible by 11, which of the following is not necessarily a divisor of X?

A. 12
B. 22
C. 24
D. 33
E. None of these
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E
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If x is a product of 4 consecutive integers, and x is divisible by 11 07 Nov 2024, 08:09
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Hi, any explanations here ?
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If x is a product of 4 consecutive integers, and x is divisible by 11 08 Nov 2024, 08:26
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consecutive integers are x,x+1,x+2,x+3= x(1+2+3+4)=10x which is divisible by 11 and.x is multiple of 11 so just for readability take 10x mulyiplied by 11 as 1100x now all options divide 1100 so none of these are not divisors of it.
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If x is a product of 4 consecutive integers, and x is divisible by 11 08 Nov 2024, 19:56
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Consective integers

X= (a*a+1*a+2*a+3)

Since X is factor of 11 so it will be Factor of all multiples of 11 as well its values +1,+2,+3..
Of given options all are true except option E
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If x is a product of 4 consecutive integers, and x is divisible by 11 14 Nov 2024, 12:18
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Nomayer28
If x is a product of 4 consecutive integers, and x is divisible by 11, which of the following is not necessarily a divisor of X?

A. 12
B. 22
C. 24
D. 33
E. None of these
Show more
If X = n(n+1)(n+2)(n+3) it represents the product of four consecutive integers. In any set of four consecutive integers:
- One of the numbers will always be divisible by 2
- One of the numbers will always be divisible by 3
- One of the numbers will always be divisible by 4

So we have at least 2, 3, 4 (or better 2^2), 11 as factors of X

So we look at the solutions

12: This factors into 2^2 * 3. We have this in our bag of prime factors
22. This factors into 2 x 11. We have this in our bag of prime factors
24. 2^3 x 3. We have this
33. 3 x 11. We have this

Since X is divisible by each of the four A-D, the answer is E: none of these
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If x is a product of 4 consecutive integers, and x is divisible by 11 15 Jan 2025, 22:14
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Jet32100 / Bunuel / KarishmaB how did you conclude this? Is this some basic theory or logical interpretation?

- One of the numbers will always be divisible by 2
- One of the numbers will always be divisible by 3
- One of the numbers will always be divisible by 4

Jet32100
Nomayer28
If x is a product of 4 consecutive integers, and x is divisible by 11, which of the following is not necessarily a divisor of X?

A. 12
B. 22
C. 24
D. 33
E. None of these
If X = n(n+1)(n+2)(n+3) it represents the product of four consecutive integers. In any set of four consecutive integers:
- One of the numbers will always be divisible by 2
- One of the numbers will always be divisible by 3
- One of the numbers will always be divisible by 4

So we have at least 2, 3, 4 (or better 2^2), 11 as factors of X

So we look at the solutions

12: This factors into 2^2 * 3. We have this in our bag of prime factors
22. This factors into 2 x 11. We have this in our bag of prime factors
24. 2^3 x 3. We have this
33. 3 x 11. We have this

Since X is divisible by each of the four A-D, the answer is E: none of these
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If x is a product of 4 consecutive integers, and x is divisible by 11 15 Jan 2025, 22:17
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Sujithz001
Jet32100 / Bunuel / KarishmaB how did you conclude this? Is this some basic theory or logical interpretation?

- One of the numbers will always be divisible by 2
- One of the numbers will always be divisible by 3
- One of the numbers will always be divisible by 4

Jet32100
Nomayer28
If x is a product of 4 consecutive integers, and x is divisible by 11, which of the following is not necessarily a divisor of X?

A. 12
B. 22
C. 24
D. 33
E. None of these
If X = n(n+1)(n+2)(n+3) it represents the product of four consecutive integers. In any set of four consecutive integers:
- One of the numbers will always be divisible by 2
- One of the numbers will always be divisible by 3
- One of the numbers will always be divisible by 4

So we have at least 2, 3, 4 (or better 2^2), 11 as factors of X

So we look at the solutions

12: This factors into 2^2 * 3. We have this in our bag of prime factors
22. This factors into 2 x 11. We have this in our bag of prime factors
24. 2^3 x 3. We have this
33. 3 x 11. We have this

Since X is divisible by each of the four A-D, the answer is E: none of these
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Yes, it is both. Explained here: https://anaprep.com/arithmetic-factors- ... -integers/
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