sum of the roots = a.
product=b.
if b is prime number, one root=1 and other=b
thus a = b+1.
24=23+1 possible.
29=28+1 nopes
57=56+1 nopes
40=39+1 nopes
92=91+1 nopes
IMO A
roots
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
cans
- Legendary Member
- Posts: 1309
- Joined: Mon Apr 04, 2011 5:34 am
- Location: India
- Thanked: 310 times
- Followed by:123 members
- GMAT Score:750
If my post helped you- let me know by pushing the thanks button 
Contact me about long distance tutoring!
[email protected]
Cans!!
Contact me about long distance tutoring!
[email protected]
Cans!!
-
knight247
- Legendary Member
- Posts: 504
- Joined: Tue Apr 19, 2011 1:40 pm
- Thanked: 114 times
- Followed by:11 members
In a quadratic equation of the form ax2+bx+c the sum of roots=-b/a and product of roots=c/a
using this formula on x2 - ax + b = 0 we have
sum of roots=-(-a)=a ....+ve integer
product of roots=b ....which is a prime number meaning that its only factors could be 1 and itself. So the two roots are 1 and some other prime number. So sum of roots=1+some prime number.We need to find which of the answer choices would give a prime number when 1 is subtracted from them.
(A)24-1=23 YES
(B)29-1=28 NO
(C)57-1=56 NO
(D)40-1=39 NO
(E)92-1=91 NO
Hence A
using this formula on x2 - ax + b = 0 we have
sum of roots=-(-a)=a ....+ve integer
product of roots=b ....which is a prime number meaning that its only factors could be 1 and itself. So the two roots are 1 and some other prime number. So sum of roots=1+some prime number.We need to find which of the answer choices would give a prime number when 1 is subtracted from them.
(A)24-1=23 YES
(B)29-1=28 NO
(C)57-1=56 NO
(D)40-1=39 NO
(E)92-1=91 NO
Hence A
-
sl750
- Master | Next Rank: 500 Posts
- Posts: 496
- Joined: Tue Jun 07, 2011 5:34 am
- Thanked: 38 times
- Followed by:1 members
Ok, I screwed it up
Sum of roots x1+x2 = a
The factors for a prime number are the number itself and 1.
We need a number for a, for which a-1 is a prime number
For a=24 b=23; x^2-24x+23=0 Can be expressed as the factors of the prime number 23 (x-23)(x-1)
Sum of roots x1+x2 = a
The factors for a prime number are the number itself and 1.
We need a number for a, for which a-1 is a prime number
For a=24 b=23; x^2-24x+23=0 Can be expressed as the factors of the prime number 23 (x-23)(x-1)
-
tpr-becky
- GMAT Instructor
- Posts: 509
- Joined: Wed Apr 21, 2010 1:08 pm
- Location: Irvine, CA
- Thanked: 199 times
- Followed by:85 members
- GMAT Score:750
To factor the quadratic we know that b = the product of the roots and a = the sum of the roots. The signs are controlled by the signs in the equation - if the last sum is positive then the roots are either both positive or both negative, add that to the negative in front of the second term means that each of the roots are positive.
The fact that b = the product of the roots and that b is prime means that b is a multiple of a prime number and 1. thus the sum of the roots is going to be a prime plus one.
That means to subtract 1 from each of the answers and figure out which result is prime. Only A creates this result.
The fact that b = the product of the roots and that b is prime means that b is a multiple of a prime number and 1. thus the sum of the roots is going to be a prime plus one.
That means to subtract 1 from each of the answers and figure out which result is prime. Only A creates this result.
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Master GMAT Instructor
The Princeton Review
Irvine, CA
