SGP

How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime?
(A) zero
(B) One
(C) Two
(D) Three
(E) Four

The answer is D, but I thought the answer would be E.

Don't these 4 numbers meet the condition? If you can explain why the answer is D, please help!

21 = 3 x 7
22 = 2 x 11
23 = 23 x 1
29 = 29 x 1

Tsenguun

1 isn't a prime number. So you should eliminate 23 and 29. And those 4 numbers would be, imo, 21 = 3 x 7, 22 = 11 x 2, 25 = 5 x 5, 26 = 13 x 2;

pmahesh107

tsenguun is wrong for 25 = 5 x 5 tehres only 3 because it said 2 DIFFERENT prime numbers

Tsenguun

sry, i didn't notice that. kk

aisgzdavinci

wondering how that will relate to real life

SGP

You have been very helpful and I learned something! I always thought 1 was prime....now I know!

shuaishuaishuai

shouldn't the answer be zero becuase of the conditions are that each integer is the product of exactly two different number and 21=3*7 or 1*21

wis3ly

21 x 1 doesn't work because 1 is not a prime number. 1 x 1 =1

shuaishuaishuai

that's not the point. the point is that 21 is not a integer that's the product of EXACTLy two different numbers. Therefore, the answer to the question should be zero, no number from 20 to 30 fits the description.

Ren the SAT'er

^wrong, please try again.

shuaishuaishuai

what are you saying Ren the SAT, according to you people, if 21 can be counted because 3*7=21 why couldn't 2*13=26 count? 2*11=22 counts also.

fignewton

^I'm not sure what you're unclear about, but here is the list. We want exactly two different prime numbers:

21 = 3 x 7 yes
22 = 2 x 11 yes
23 = 1 x 23 no since 1 is not a prime number by convention
24 = 2 x 2 x 2 x 3 no too many
25 = 5 x 5 no not different
26 = 2 x 13 yes
27 = 3 x 3 x 3 no too many
28 = 2 x 2 x 7 no too many
29 = 1 x 29 no since 1 is not a prime number by convention

Three yes numbers.