SAT question?

Question

If n and p are integers greater than 1,and p is a factor of both n+3 and n+10 ,what is the value of p?

A. 3 B. 7 C. 10 D. 13 E. 30


Explain.

Answer 1

i'd say B. because the difference between n + 10 and n + 3 is 7.

multiples of a number have a difference of that number.
for example, multiples of 3 (3, 6, 9, 12, etc) all are 3 apart from each other.

n+3 and n+10 are multiples of p.
the difference between n + 3 and n + 10 is 7, therefore p is 7.

this question is a lot more about logic than math, so it's kind of hard to explain the reasoning behind the logic. you could also plug in numbers and do guess and check, but that would take a while (unless you get lucky).

Answer 2

When you see questions with variables, PLUG IN!

In your example, we have a rule for N and P - they are integers greater than 1.

Now it says "p is a factor of both n+3 and n+10."

So we plug in for N. Let's pick 2, that's an easy number.
2+3 = 5. 2+10 = 12. Hmm, that doesn't give us easy factors.

Let's pick something else.
if N=11, then: 11+3 = 14 and 11+10=21.

7 is a factor of both 14 and 21. So our P is 7. (It also satisfies the rule of being an integer greater than 1.)

Is 7 one of the answer choices? Yep! There you go.

Answer 3

The only number that you can factor and get both a 10 and 3 would be 30 - E

Answer 4

p=7. n = 4, 11 or 18.

explanation: i used substitution. i started with multiples of 3, and deduced that it would be impossible for any value of n to fulfill the variables. with 7, i plugged in 18, and it worked. to check, i plugged in 11 as n, and it also worked.

Answer 5

n>1, p>1, n+3/n+10=p/p(same ratio), p=13,i don't know if it is correct.

Answer 6

the answer is 7

Answer 7

a