Target question: What is the value of W?

Given: W, X, Y, and Z represent distinct digits such that (WX)(YZ) = 1995
Let's take a close look at what we can conclude from this info.
Whenever I see a big number like 1995, I consider finding its PRIME FACTORIZATION
1995 = (3)(5)(7)(19)
In what ways can we take this and rewrite 1995 as the product of two 2-digit integers?
We get 4 possible cases;
(WX)(YZ) = 1995
a) (21)(95) = 1995
b) (95)(21) = 1995
c) (35)(57) = 1995
d) (57)(35) = 1995

HOWEVER, since all 4 digits must be DISTINCT, we must eliminate cases c and c, which leaves us with only 2 possible cases.
(WX)(YZ) = 1995
a) (21)(95) = 1995
b) (95)(21) = 1995

Statement 1: X is a prime number
Since 1 is not prime, we can rule out case a.
This leaves only case b, which means W must equal 9
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Z is not a prime number
1 is the only NON-PRIME number, so this rules out case a.
This leaves only case b, which means W must equal 9
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer =

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Given WX * YZ = 1995

With Statement (1), knowing X is prime does not help us determine W. We know that either X or Z has to be 5, but we dont know which one.

With Statement (2), we are told Z is not prime. This means X has to be 5, which is prime (Note that we don't need to know statement 1 here).

Prime factors of 1995 are 3, 5, 7 and 19.

In order for our product to have a 5 in the units digit, we need an odd number to multiply by 5.

If Z is not prime, then it can be either 1 or 9 (rest of the odd integers are prime)

We know so far: W5 * Y(1 or 9) = 1995

Two possibilities: If X is 9, then YZ = 19 (one of the prime factors). But we would need WX to be 105 (3*5*7), which does not make sense.

The other option is that X is 1, which gives us YZ = 21 (3 * 7). Now WX is 95 (5*19) and this satisfies our two digit constraint. Thus W is 9.

Answer is B (Statement 2 alone)

Please let me know if I committed an error in my thinking.

Factors of 1995 are 5 * 3 * 7 * 19 and also given that WX * YZ = 1995.. we are not sure which all factors take the values of w,x,y and z respectively.

Stat 1: X is a prime number , we have four different prime numbers... Insufficient.

Stat 2: Z is not a prime number..there is no such number...Insufficient...

IMO E is correct answer.

OA please...will correct if I missed anything.

The Option is D .Because W,X,Y,Z are distinct numbers so in the above scenario case C & D will not exist. 1 is not prime so only option is 95*21.

Good catch. I carelessly missed the word "distinct"
I've edited my response.

Cheers and thanks,
Brent
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What is the best way to solve this under two minutes? How are we to recognize such questions - any leads to similar questions?
VeritasPrepKarishma Bunuel

Hi..

factorize 1995..
\(1995=3*5*7*19\)
now 19 has to be multiplied with another prime factor otherwise the other integer becomes 3 digit integer 105.. 19*105
so possiblities--
1)19*3 and 5*7 that is 57 and 35... NOT possible as 5 is repeated
2) 19*5 and 3*7 that is 95 and 21.. possible
3) 19*7 and 3*5... NOT possible as 19*7 becomes 3-digit integer

WX can be 95 or 21..
so W can be 9 or 2

lets see the statements..
(1) X is a prime number
If X is prime WX has to be 95... so W is 9
suff

(2) Z is not a prime number
If Z is not prime, YZ must be 21.
so WZ is 95 and W is 9
suff

D
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D is the Answer

factorization of 1995 yields 5x3x7x19 of which 95x21 is the combination we are interested in.

95x21=1995
the distinct digits are 1,2,9,5
w9 x5 y2 z1

1) X is prime = 95x21=1995 , w=9 , hence A or D. ( where X=5)
2) Z is not prime= 95x21=1995, w=9 hence Only D (where Z = 1) ( Therefore A is rejected)

chetan2u please correct the OA. The answer should be B, as explained above.

1995 = 3*5*7*19
The only two digit couples that can be formed are
35*57
21*95
from statement 1, x is prime
it could be either of the two pairs as both have atleast one number with 5 as unit's digit.

statement 2, z isn't prime.
Only 21*95 will qualify. 1 is neither prime nor composite.

Statement 1 can easily qualify for both of the two.
Isn't 7 prime? Isn't 5 prime? Then, what's wrong with 35*57?
Why only 95?
The statement isn't saying that "ONLY" x is prime, right?

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