abc is a three digit number where a is the hundreds digit, b is the tens digit, and c is the units digit. Let &(abc)& = (2^a* 3^b*5^c). For example, &(203)& = (2^2)(3^0)(5^3) = 500. How many three digit numbers abc will give a prime number when the formula &(abc)& is applied?
A) 0 B) 1 C) 2 D) 3 E) 9
I did not understand what question is trying to ask.
GMAT Forum
5 postsPage 1 of 1
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
Re: primes
Per the forum rules, we need a citation of the oiginal source of the problem.
Please provide this citation, and please read through the forum rules as well. Thank you.
Please provide this citation, and please read through the forum rules as well. Thank you.
- LauraS862
- Course Students
- Posts: 2
- Joined: Sat Aug 16, 2014 2:56 pm
Re: primes
Hi! I also had a question on this as I am either not understanding the concept or the explanation. It is #20 on the Divisibility & Primes Drill worksheet. I received mine as part of a PEA...
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
Re: primes
ok.... technically, this thread should have been posted in the MGMAT non-CAT folder. but, to avoid further delays, let's keep it here.
here are the basics:
• the thing with the "&" symbols (on here-- it may have been a different symbol on the paper, doesn't really matter) is like a machine.
– you put a 3-digit number in
– you get a number out.
the "number out" is made by powers of 2, 3, and 5, as described. it's 2 raised to the 100's digit, times 3 raised to the 10's digit, times 5 raised to the 1's digit.
so, for instance, if you put the number 213 into the "machine", it spits out 2^2 times 3^1 times 5^3, which is 1500.
this symbol does exactly the same thing that "f(x)" would do, by the way. if it helps you to take out the symbol and put "f( )" in its place, you can do that.
here are the basics:
• the thing with the "&" symbols (on here-- it may have been a different symbol on the paper, doesn't really matter) is like a machine.
– you put a 3-digit number in
– you get a number out.
the "number out" is made by powers of 2, 3, and 5, as described. it's 2 raised to the 100's digit, times 3 raised to the 10's digit, times 5 raised to the 1's digit.
so, for instance, if you put the number 213 into the "machine", it spits out 2^2 times 3^1 times 5^3, which is 1500.
this symbol does exactly the same thing that "f(x)" would do, by the way. if it helps you to take out the symbol and put "f( )" in its place, you can do that.
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
Re: primes
now, the problem is asking about getting a prime number OUT of the machine.
• the primes involved here are 2, 3, and 5.
• for the output to be prime, the output itself has to be 2, 3, or 5.
note that
2 = (2^1)(3^0)(5^0)
3 = (2^0)(3^1)(5^0)
5 = (2^0)(3^0)(5^1)
there won't be any other prime outputs.
• to get 2, you'd put 100 into the machine (giving you (2^1)(3^0)(5^0) = 2). that's legit.
• to get 3, you'd have to put in "010", but that's not a three-digit number. (it's 10, which is a two-digit number.) so, nope.
• can't get 5 either. (you'd have to put in "001", but that's actually a one-digit number.)
• the primes involved here are 2, 3, and 5.
• for the output to be prime, the output itself has to be 2, 3, or 5.
note that
2 = (2^1)(3^0)(5^0)
3 = (2^0)(3^1)(5^0)
5 = (2^0)(3^0)(5^1)
there won't be any other prime outputs.
• to get 2, you'd put 100 into the machine (giving you (2^1)(3^0)(5^0) = 2). that's legit.
• to get 3, you'd have to put in "010", but that's not a three-digit number. (it's 10, which is a two-digit number.) so, nope.
• can't get 5 either. (you'd have to put in "001", but that's actually a one-digit number.)
5 posts Page 1 of 1