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25 Oct 2010, 11:17
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If n = 2×3×5×7×11×13×17, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. Is even (n + 4)/2 = even
A. I only
B. II only
C. III only
D. I and III only
E. None
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-2-3-5-7-11-13-17-then-which-of-the-following-statements-must-b-195397.html
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. Is even (n + 4)/2 = even
A. I only
B. II only
C. III only
D. I and III only
E. None
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-2-3-5-7-11-13-17-then-which-of-the-following-statements-must-b-195397.html
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25 Oct 2010, 11:33
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shrive555
If n = 2×3×5×7×11×13×17, then which of the following statements must be true?
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
A- I only
b- II only
C- III only
D I and III only
e None
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
A- I only
b- II only
C- III only
D I and III only
e None
(I) 2×3×5×7×11×13×17/600 = 7x11x13x17/20 => n is NOT divisible by 600
(II) n + 19/19 => n/19 + 1
as 19 is a prime number and n does not have 19 as factor => n is NOT divisible by 19.
so n+19 is NOT divisible by 19
(III) n+4/2 = n/2 + 2
= 2×3×5×7×11×13×17/2 + 2
= 3×5×7×11×13×17 + 2
The number 3×5×7×11×13×17 is ODD (since Odd * Odd = Odd)
So Odd + 2(even) = Odd
Hence n+4/2 is NOT Even
Answer (E)
25 Oct 2010, 12:19
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shrive555
If n = 2×3×5×7×11×13×17, then which of the following statements must be true?
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
A- I only
b- II only
C- III only
D I and III only
e None
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
A- I only
b- II only
C- III only
D I and III only
e None
I) 600=2^3*3*5^3 ... n^2 will only have 2 powers of 5 and 2, so will not be divisible by 600
II) n is not divisible by 19 (19 is a prime number), so neither can n+19 be divisible by 19.
III) (n+4)/2 = (n/2) + 2 .... (n/2) is not even. Odd+Even = Odd. Hence not true
Answer is none
