hard question from kaplan gmat DS chapter...

[davedecibel]

[please note that =< stands for "less than or equal to"]

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If z is an integer, is z prime?

(1) 15! < z

(2) 17! + 2 =< z =< 17!+17
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i read the solution on the book, it might be because it's night and i'm tired now, but i didn't understand the explanation at all.....i suck at number properties O_o

could you tell me how long does it take you to figure out the right answer, and how do you do it?????i'm lost!

[davedecibel]

ok after i read the explanation more carefully i got it... still, it's not really intuitive. maybe some of you can find out a better way? i'm curious....

[TOPGMAT]

Whats the ans ? Is it B?

17! + 2 = 17*16*....3*2*1 + 2 = 2(Z+1) =>divisible by 2... Hence not prime...
Similarly every other number can be grouped...
Except if the question was 17!+1... In that case I don't know how to proceed.

[goyalsau]

Whats the ans ? Is it B?

17! + 2 = 17*16*....3*2*1 + 2 = 2(Z+1) =>divisible by 2... Hence not prime...
Similarly every other number can be grouped...
Except if the question was 17!+1... In that case I don't know how to proceed.

Even i suppose to write this

17! + 1 , will not be divisible by any number from 2 to 17,

I think answer of this question should be B,

and please Daved , please share the Official explanation,
I am sure that will help a lot, till we don't have any other source of information..

[selango]

stmt1,

15!<Z

No info about Z

Insufficient

stmt2,

17! + 2 <= z <= 17! + 17

17! = 1*2*3*...17

17!+2 = 2(1+1*3*..........17)

17! +2 is divisible by 2 .. not prime

Similarly check for 3,4,5....17

17! +3 is divisible by 3.. Not prime

17! +4 is divisible by 4..not prime

.......
....
17! +17 is divisible by 17.. not prime

Sufficient.

Pick B

[davedecibel]

you guys got it perfectly right, b is the correct answer, and the reasoning behind that is perfect.

i have some difficulties in such questions... do you think that manhattan "number properties" book would help me out on these topics?

[davedecibel]

and please Daved , please share the Official explanation,
I am sure that will help a lot, till we don't have any other source of information..

the original explanation is pretty much the same you all figured out, it's just written badly imo O_o

[goyalsau]

I there any way by which we can figure out Whether 17! + 1 is a prime number or not.

[Brian@VeritasPrep]

Hey guys,

Great thread, and the answer is indeed B for the reasons everyone discussed. If you're interested, we actually had a great conversation about this one a few months ago that may have delved even further into it. Take a look:

https://www.beatthegmat.com/prime-numbers-t62545.html

[goyalsau]

Hey guys,

Great thread, and the answer is indeed B for the reasons everyone discussed. If you're interested, we actually had a great conversation about this one a few months ago that may have delved even further into it. Take a look:

https://www.beatthegmat.com/prime-numbers-t62545.html

Thanks Brian,
I got my answer.........