Primers

Level pending

Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?

181 231 119 69

Rohan Chandra by Rohan Chandra , 24, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Raghav Dua
Jan 25, 2014

The primes between 4 and 18 are: 5, 17, 11, 13, 17

A total of 20 different combinations can be formed for multiplication, so using a trial and error method is feasible.

After some trials, we realize that (11 x 13) - (11 + 13) = 143 - 24 = 119 , hence the answer.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice one (y), well are you in 12th ?

Rohan Chandra - 7 years, 4 months ago

Yah man. You?

Raghav Dua - 7 years, 4 months ago

Log in to reply

same here ! 12th ! I'm in Delhi, what about you?

Rohan Chandra - 7 years, 4 months ago

Log in to reply

You're in 12th? It says you're 16. Gurgaon

Raghav Dua - 7 years, 4 months ago

Log in to reply

@Raghav Dua – yup ! Thats right, I started my education early, no worries, many people are having the same issue. Gurgaon (y) nice.

Rohan Chandra - 7 years, 4 months ago
Rohan Chandra
Jan 25, 2014

Let the primes be p and q. The problem asks us for possible values of K where K=pq - p - q

Using Simon's Favorite Factoring Trick:

K+1=pq - p -q + 1 K+1= (p - 1 )(q - 1) Possible values of (p - 1) and (q - 1) are: 4,6,10,12,16

The possible values for K+1 (formed by multipling two distinct values for (p - 1) and (q - 1)) are: 24,40,48,60,64,72,96,120,160,192

So the possible values of K are: 23,39,47,59,63,71,95,119,159,191

The only answer choice on this list is 119 \boxed{119}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...