Number Properties

[tonebeeze]

Is P divisible by 11?

1. 10 - p = 3q

2. 3q + 12 is divisible by 11

OA = C

[srcc25anu]

where's the Question stem?

[HSPA]

use A and add 12 on both sides

10-p+12 = 3q+12
we know 3q+12 is divisible by 11 from B and on LHS you can see 22 which is divisible by 11
s0 p = 22 -(3q+12)

=> P is divisible by 11..

C it shall be

[MAAJ]

Is P divisible by 11?

1. 10 - p = 3q
- p = 3q - 10
p = -3q + 10
we don't know what "q" is so insufficient

2. 3q + 12 is divisible by 11
Doesn't tell us anything about P so insufficient

1. And 2. Combined:
(3q) + 12 is divisible by 11
(10 - p) + 12 is divisible by 11
-p + 22 is divisible by 11
Dividing (-p + 22) by 11 must provide an integer
-p/11 + 22/11 = -p/11 + 2 AND -p/11 must be an integer
So -p and p must be divisible by 11

[tpr-becky]

"divisible by" is code words for factoring - so the real question is "does p have 11 as a factor?"

Look at stmt 1:

we can rearange to find that 10-3q = p. No where in the stem does it say that P is an integer so P can be any nubmer and q can be any number so this is insufficient - you have B C E left.

Stmt 2- this statement doesn't contain any information about P so it's can't work - C E are left.

together - we have to combine - if 10-p =3q and 3q + 12 is divisible by 11 - can can find that 10-p+12 is divisible by 11

so 22-p is divisible by 11 - since 22 is divisible by 11 then that means P must also be - BUT you don't even really need to go that far - 11 is prime and you know that 22-p is divisible by 11 and because this is a YES/No Data sufficiency you know you could solve it so C is the answer regardless.