Integers

I felt this one to be a toughie for under 2 minutes(to come up with examples). Took me a little more than 3 so defnitely need to improve on that part

Here it goes:

x<y<z and x,y,z are consecutive integers
x+y+z is divisble by 10 so their sum must end in 0 i.e their units digit sum must end in 0

1 2 3 4 5 6 7 8 9 0

Only possible combination is 9 0 1 satisafying all conditions above


Stmt I

y is divisible by 6


29 30 31 - > yes
119 120 121->NO

Stmt II

z is prime

9 10 11->no
29 30 31-> yes

TOGETHER

29 30 31-> YES
299 300 301-> NO

Choose E

4meonly wrote:OA E

x=n y= x+1 z= x+2

x+y+z = 3x+3 = 3(x+1) = 10k

(1) y is divisible by 6

x+1 = 6l

3(x+1) = 10k -->

3*6l = 10k

clearly l must be multiple of 5 i.e l= 5n

x+1 = 6*5n = 30n

n=1
x+1 = 30 --> x=29 --> prime number
n=4
x+1 = 120 x=119 --> not a prime number

(ii)

z is prime number

9 10 11 --> x not a prime number
29 30 31 -- > x is prime number

alone not sufficient

Combined

x=149 y=150 z=151 --> x prime number