If n = 2×3×5×7×11×13×17, then which of the following statements must b

Question

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. (n + 4)/2 is even

A. I only
B. II only
C. III only
D. I and III
E. None of the above

Kudos for a correct  solution .

AmoyV · Accepted Answer

St 1: 600=2^3*3*5^2
We have only 1 factor of 2 in n. n^2 will not solve this problem and hence n^2 can be divisible by 600---->Not True

St 2: n is not divisible by 19 so n+19 wont be divisible by 19---->Not True.

St 3: Can be written as (n/2)+2; n=2*Odd
(n/2)=2*Odd/2=Odd; 
(n/2)+2=Odd + 2 = Odd (Not Even)--->Not True

Answer: E

gmatgrl · Answer

I. 600 = 3*2*2*2*5*5
n^2 will only have two occurances of 2, but what is required are "three" instances of 2 (to be divisible by 600). So, this is not correct.

II. For n + 19 to be divisible by 19, n must be divisible by 19; however, clearly n is not divisible by 19. So, this is not correct.

III. (n + 4)/2 = n/2 + 2. Now, n/2 is not even. So, we have a situation of odd + even, which is odd. So, this is not correct.

So, looks like none.

Lucky2783 · Answer

I. n^2 is divisible by 600 
 N^2 = 900 * 7×11×13×17*7×11×13×17 clearly not divisible by 600

II. n + 19 is divisible by 19
 n is even and  \frac{(E+19)}{19} will not be an integer.

III. (n + 4)/2 is even
 n is 2*ODD , (2*ODD +4 )/2 = ODD + 2 = ODD

Answer E

OptimusPrepJanielle · Answer

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. (n + 4)/2 is even A. I only B. II only C. III only D. I and III E. None of the above Statement I: 600 = (2^3)*(3)*(5^2) n^2 will have 2 factors of 2 but 600 has 3 factors of 2. So this is NOT true. Statement 2 Since n is not divisible by 19 so n+19 is also NOT divisible by 19. So this is NOT true. Statement 3: (n+4)/2 = n/2 + 2 Now, n/2 is divisible by 2 since it contains 2. The remainder is 3*5*7*9*11*13*17 which is ODD. So, ODD + 2 cannot be even. So this is NOT true. Hence option (E). -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

SherLocked2018 · Answer

I. since n has 2, 3, 5 one time, n^2 will have 2,2,3,3,5,5. But to be divisible by 600 completely, it should have three 2's, (since 600 = 6*10*10 = 2.3.2.5.2.5) 
Thus I is not true.

II. n+19 is divisible by 19, if n is divisible by 19 too, which clearly n is not. thus II is not true.

III. we know (n+4)/2 = n/2 + 2 = odd + even = odd. Thus III is also not true.

ans None = E.

PareshGmat · Answer

Answer = E. None of the above

I. n^2 is divisible by 600

600 = 2^3 * 3^1 * 5^2

n^2 = 2^2 * 3^2 * 5^2  (Only the factor component)

This condition fails

II. n + 19 is divisible by 19

n does not have any factor of 19

This condition fails

III. (n + 4)/2 is even

\frac{n+4}{2} = \frac{n}{2} + 2

n has only 1 factor of 2, so after dividing by 2, remaining is ODD

ODD + EVEN = ODD

This condition fails as well

lipsi18 · Answer

1. n^2 = 100*3*3*(7*11*13*17)^2 is not divisible by 100 but not by 6 so not divisible by 600
2. Is n divisible by 19? no; n=2*3*5*7*11*13*17. so (n+19) is also not divisible by 19
3. n/2+2 =even; n has only one 2 so n/2 is odd; odd+2= odd; not even

Hence None of the options are correct.
Answer is E.

Thanks

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: whichmustbetrue_text.PNG FAQ: If option III is divisible by 2, isn't it even? Let's look again at what exactly this question asks for: which of the statements, after all the math is carried out , are even? 2*3*5*7*11*13*17 + 4 is divisibly by 2, yes, and that means it's even. But statement III asks about the result of (2*3*5*7*11*13*17 + 4) / 2. After the division by 2 is carried out, we are left with an odd number: 3*5*7*11*13*17 + 2 After we divide out that 2, the numbers that are left in the numerator don't add up to an even number.

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If n = 2×3×5×7×11×13×17, then which of the following statements must b

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