For positive integers x and y, x=19!+y. Is x a prime number?

Question

(1) 41>y>37
(2) y is even

stonecold · Answer

Given data -> x=19!+y
We need to see if x is prime or not.

Statement 1=>
y can be 38,39,40

If y=38 => x=2*(some integer) => Non prime
y=39=> x=13*(some integer) => Non prime 
y=40 => x=2*(some integer) => Non prime

Basically the logic used here is that PRIMES cannot be subdivided (other than off course--> Prime*1).
Hence x is not a prime.

Hence Sufficient.

Statement 2=>
If y is even => x=2*(some integer)=> Again => Non prime.

Hence x can never be prime.
Hence Sufficient.

Smash that D.

NOTE-> all some integers are greater than 1

chetan2u · Answer

Hi..

x=19!+y ...
When will x be prime Or even better and easier here when will it be NOT a prime
 when y contains any factor SAME as of 19! And 19! Has all factors from 2 to 19

Let's see the statements..
1) 41>y>37..
Y can be 38,39 or 40..
If 38 or 40, Common factor will be 2..
If 39, common factor will be 3..
In every case and is NO
Sufficient

2) y is Even..
In every case, common factor will be 2..
So x is multiple of 2
Ans is NO always 
Sufficient

D

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 2 variables and 1 equation, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) The possible values of y are 38, 39, 40. If y=38=2*19 , we have 19!+38 = 19! + 2*19 = 18!*19 + 2*19 = (18!+2)*19 , which is not a prime number. If y=39=3*13 , we have 19!+39 = 1*2*3*4*...*19 + 3*13 = 3*(2*4*5*...*19) + 3*13 = 3*((2*4*5*...*19)+13) , which is not a prime number. If y=40=2*20 , we have 19!+39 = 1*2*3*4*...*19 + 2*20 = 2*(3*4*5*...*19) + 2*20 = 2*((3*4*5*...*19)+20) , which is not a prime number. Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient. Condition 2) If y=2*k , we have 19!+2k = 1*2*3*4*...*19 + 2k = 2*(3*4*5*...*19) + 2k = 2*((3*4*5*...*19)+k) , which is not a prime number. Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient. Therefore, D is the answer. If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

pappal · Answer

whether x=19!+y is prime or not?
2. 19! will be an even number with certain no of zeroes in the end ,adding an even number to it will certainly result in an even number so x is absolutely not a prime SUFFICEINT
1. given y=38 or 39 or 40
38 and 40 are both even so x for them will be an even no. so not a prime
now if we take y=39
x=1* 2 *3*4*5....... 19  + 39= 38(1*3*4*5........*18+1) is a multiple of 38 so not a prime 
so SUFFICIENT
hence D

For positive integers x and y, x=19!+y. Is x a prime number?

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GMAT Data Sufficiency (DS) Questions

For positive integers x and y, x=19!+y. Is x a prime number?

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