Find integer W. (1) W is a prime solution of (|W|)!=|W| (2)

Question

Find integer W. (1) W is a prime solution of (|W|)!=|W| (2) W is a prime solution of W!–|W|=0 And show this integer! :wink:

prashant · Answer

(1) gives the solution set as {-2, -1, 1, 2}

(2) gives the solution set as {1,2}

Therefore E

stolyar · Answer

E is clearly wrong
(1) gives the solution set as {–2, –1, 1, 2}; 2 is the only prime solution
(2) gives the solution set as {1, 2}; 2 is the only prime solution

W=2
Therefore, it is D.

prashant · Answer

Agreed - I drew the wrong inference :oops:

mathewmithun · Answer

Hi, I was going thru the old question that were shared... can some one explain  prime solution? ...thanks in advance

Bunuel · Answer

Not a GMAT wording.

"W is a prime solution" simply means that  w  is a prime number.

So basically the question is:

If w is a prime number, then what is the value of w?

(1)  (|W|)!=|W|  --> solutions are: -1, 1, -2 and 2. Only one of these values is prime: 2. Hence  w=2 . Sufficient.

(2)  W!-|W|=0  --> solutions are: 1 and 2. Only one of these values is prime: 2. Hence  w=2 . Sufficient.

Answer: D.

jlgdr · Answer

So I guess prime numbers can't be negative no? Cheers J

Bunuel · Answer

Only positive numbers can be primes. So, the smallest prime number is 2.

hysenkoshy · Answer

How is 1 a solution.. 1! Is 0 which is not equal to absolute value of 1. So IMO, there are only 2 solutions. 2 and -2. And one prime number

Bunuel · Answer

_____________
1! is NOT 0. 1! = 1.

cnbcravi · Answer

E is clearly wrong 
(1) gives the solution set as {–2, –1, 1, 2}; 2 is the only prime solution 
(2) gives the solution set as {1, 2}; 2 is the only prime solution

W=2 
correct answer is D.

hysenkoshy · Answer

Oops !! Sorry ... My bad.. 0! Is 1 , right ? Got confused !!

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Find integer W.

(1) W is a prime solution of (|W|)!=|W|
(2) W is a prime solution of W!–|W|=0

In the original condition, there is 1 variable(w), which should match with the number of equation. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), w=2, which is unique and sufficient
For 2), w=2, which is unique and sufficient.
Therefore, the answer is D.

l For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

bumpbot · Answer

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Find integer W. (1) W is a prime solution of (|W|)!=|W| (2)

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Find integer W. (1) W is a prime solution of (|W|)!=|W| (2)

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