If r and s are positive integers and r = s + 2, is r + s divisible by

Question

If r and s are positive integers and r = s + 2, is r + s divisible by 4?

(1) r is a prime number.
(2) s is a prime number.

A new tricky DS Question

broall · Answer

If r and s are both even, then r+s isn't divisible by 4.
If r and s are both odd, then r+s is divisible by 4.

(1) r is a prime number.

r = s+2 so r > 2. Hence r must be odd, so s must be odd.

Thus, r+s is divisible by 4. Sufficient.

(2) s is a prime number.

If s=2, then s is even and r is even. Thus r+s isn't divisible by 4.
If s=3, then s is odd and r is odd. Thus r+s is divisible by 4.

Insufficient.

Answer A.

vs224 · Answer

Ans is B.
r+s = 2(s+1) via substitution of r= s+2

if s is odd/prime, then r+2 should be divisible

On the other hand, 2(r-1)   will not work with if r is 2, work if r =3

asthagupta · Answer

A??
r+s = 2(s+1)
st1> r is prime, so s is also odd as r cannot be 2(if r=2 then s=0). Other than 2 for every prime R, S will be odd. Odd + 1 is even so S+1 is even.
Even * 2 will be a multiple of 4.
suff
St2> If s is prime, S+1 will be even,
Even * 2 will be a multiple of 4.

But if S=2, then r=4.
in-suff

hence A
Please tell OA, my exam is on 15th of this month

niks18 · Answer

r+s = r+r-2  (as  r=s+2 , so  s=r-2 )
This implies:  2r-2=2(r-1) . 
hence  \frac{(r+s)}{4} = \frac{2(r-1)}{4} = \frac{(r-1)}{2} ------------- (1) 
So for  (r+s)  to be divisible by  4 ,  r  needs to be  ODD

Statement 1 : this implies that  r  is  ODD . Hence  sufficient 
( note :  r= s+2  and  s  is a positive integer, hence  s  cannot be  0 , so  r    cannot   be  2 , the only even prime no)

Statement 2 : if  s =2 , then  r=4 = Even , hence equation  (1)  is not divisible by  4 
but if  s =  odd prime no for eg.  3 , then  r = 5 = Odd , hence equation  (1)  is divisible by  4 . Hence the statement is  Insufficient

Option  A

AlexGmat2017 · Answer

B.
r + s : 4 is equivalent to (r + s) : 4 =(s+s+2):4=2*(s+2):4=(s+2):2. Hence, s must be an even number for residual to be equal to 0.

niks18 · Answer

Hi  AlexGmat2017

as per statement 2 "s" is prime no so it can be even for eg. 2 or it can be odd for eg. 3. the highlighted section is not always true

kaulshanx · Answer

A . R=s+2, statement 1 - r is prime which means s can take values of 1,3,5,9 etc so thay r would be 3,5,7,11 and so on and adding r+s would be 4,8,12,20,24 which are all multiples of 4 and hence is sufficient.
Statement 2- s is prime means s can take values of 2,3,5,7,11 etc and r cam take values of 4,5,7,9,13 and r+s takes values of 6,8,12,16,24 and so on and 6 is not divisible by 4 hence 8,12,16,24 are, hence insufficient. So answer A

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hellosanthosh2k2 · Answer

r = s + 2  =>  r - s =2

Statement 1:
  r  is prime number,  r  can't be 2, if it were, then  s = 0  but  s  is positive
 so  r  is odd prime number,
 any odd number can be written as  (2p + 1)  or  (2k + 3)  or  (2l + 5) .. where  p,k,l are integers
 Let  r = 2k + 3 , then  s = r - 2  =>  2k + 1 
 so  r + s = (2k + 3 + 2k + 1) = (4k + 4)  => which is clearly divisible by 4 => suff

Statement 2:
  s  is prime number.
 if  s = 2 => r = 4 => (r+s) = 6  not divisible by 4
 if  s  is odd prime number, we can use above method in statement 1, to prove that it is divisible by 4
 so two diff possiblities => Not Sufficient

Answer (A)

gurmukh · Answer

From first statement
R-S =2
Where R is a prime number so R is either 6k +1 or 6k-1 form where k is an integer.
Now, if R is 6k+1 form then S is 6k -1 form, so their difference is 2
Therefore R+ S = 12k 
Hence divisible by 4
Now, if R is 6k-1 form S is 6k+1 form, so their difference is 2
Therefore R + S =12k
Hence given statement is sufficient
From second statement
S is a prime number
R =3 +2 =5
R + S = 5+3=8
Divisible by 4
R = 2+2 =4
R +S = 4+2 =6
Not divisible by 4
Hence not sufficient
Therefore answer is option A

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If r and s are positive integers and r = s + 2, is r + s divisible by

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If r and s are positive integers and r = s + 2, is r + s divisible by

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