Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

QOTD#15 In the equation above, x is an integer with 3 [#permalink]
16 Nov 2016, 13:06

Expert's post

00:00

Question Stats:

75% (01:46) correct
25% (00:00) wrong based on 4 sessions

\(\frac{xz}{y}=420\)

In the equation above, x is an integer with 3 distinct prime factors, and y is a positive integer with no prime factors. If z is a positive, non-prime number, what is one possible value of z?

Re: QOTD#15 In the equation above, x is an integer with 3 [#permalink]
16 Nov 2016, 13:12

Expert's post

Explanation

Don’t forget that you can use your on-screen calculator. There’s only one positive integer with no prime factors, the number 1. Therefore, y = 1, and xz = 420. Create a prime factor tree to get the prime factors of 420: 2, 2, 3, 5, and 7. Pick 3 distinct values from that list, such as 2, 3, and 5, and multiply them to find one possible value of x. One example is 2 × 3 × 5 = 30, or one possible value for x. If 30z = 420, then z = 14. Confirm that 14 is not prime, then enter it in the field. If you chose 2, 3, 7, then x is 42 and z is 10 and also correct, and so on.
_________________

Sandy If you found this post useful, please let me know by pressing the Kudos Button

Re: QOTD#15 In the equation above, x is an integer with 3 [#permalink]
25 Nov 2016, 17:56

2

This post received KUDOS

Expert's post

sandy wrote:

\(\frac{xz}{y}=420\)

In the equation above, x is an integer with 3 distinct prime factors, and y is a positive integer with no prime factors. If z is a positive, non-prime number, what is one possible value of z?

y is a positive integer with no prime factors That should strike you as an odd statement. There's only one such number: 1 So, we already know that y = 1

So, we have (xz)/1 = 420 This means that xz = 420

When we find the prime factorization of 420, we get: 420 = (2)(2)(3)(5)(7) In other words, xz = (2)(2)(3)(5)(7)

GIVEN: x is an integer with 3 distinct prime factors So, for example, x could equal (2)(3)(5) [aka 30] Or x could equal (2)(3)(7) [aka 42] Or x could equal (3)(5)(7) [aka 105] Or x could equal (2)(5)(7) [aka 70]

If x = 30, then z = 14 If x = 42, then z = 10 If x = 105, then z = 4 If x = 70, then z = 6

So, the possible values of z are: 4, 6, 10, and 14

RELATED VIDEO

_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Dayemails

greprepclubot

Re: QOTD#15 In the equation above, x is an integer with 3
[#permalink]
25 Nov 2016, 17:56