GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 07:21

GMAT Club Daily Prep

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

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

If both roots of the quadratic equation y^2 -63y +x =0 are prime numbe

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 13 Jun 2013
Posts: 266
If both roots of the quadratic equation y^2 -63y +x =0 are prime numbe  [#permalink]

Show Tags

21 Jan 2015, 02:55
3
11
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:12) correct 48% (02:25) wrong based on 106 sessions

HideShow timer Statistics

If both roots of the quadratic equation y^2 -63y +x =0 are prime numbers then number of possible value of x is

a) 0
b) 1
c) 2
d) 4
e) more than 4
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If both roots of the quadratic equation y^2 -63y +x =0 are prime numbe  [#permalink]

Show Tags

23 Jan 2015, 14:25
3
3
Hi All,

This question is interesting in that it combines Algebra rules with Number Property rules. While you don't have to do much advanced math to answer it, you DO need to recognize the patterns that the equation is built on.

We're given Y^2 -63Y + X = 0

At first glance, this looks a bit "scary", but it should remind you of a Quadratic.

We're told that there are 2 roots and that they are BOTH PRIMES. This severely limits the possibilities....

Y^2 - 63Y + X = 0

Since the "middle term" is -63Y, the two parentheses are either BOTH negative or 1 negative/1 positive...

(Y - ?)(Y - ?) = 0

or

(Y - ?)(Y + ?) = 0

-63Y is the SUM of the roots. BOTH roots are PRIME though, so we have to think about what happens when you add/subtract odds and evens

EVEN + EVEN = EVEN
EVEN - EVEN = EVEN
ODD + ODD = EVEN
ODD - ODD = EVEN

None of these outcomes matches -63, which is an ODD number. This means that the two primes MUST be 1 odd and 1 even. The ONLY even prime is 2....so now the possibilities are...

(Y - ?)(Y - 2) = 0

or

(Y - ?)(Y + 2) = 0

To end up with -63Y as the middle term, the missing value in each of the above 2 examples would have to be.... -61 or +65....but 65 is NOT prime, so the only option is -61....

(Y - 61)(Y - 2) = 0

FOILing this out, we get...

Y^2 - 63Y + 122 = 0

X can ONLY be +122, so there's only one answer to the question.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
General Discussion
Math Expert
Joined: 02 Aug 2009
Posts: 7954
Re: If both roots of the quadratic equation y^2 -63y +x =0 are prime numbe  [#permalink]

Show Tags

21 Jan 2015, 07:16
B.... the sum of roots in the eq is 63(-b/a)... it has to be addition of an odd and an even number.... only possible value 2,61 so X becomes 2*61=122
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1751
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If both roots of the quadratic equation y^2 -63y +x =0 are prime numbe  [#permalink]

Show Tags

29 Jan 2015, 22:58

Given that both roots are prime number, it means roots cannot be even EXCEPT for 2, which is a prime number as well as a even number

In this case, only possible value of x = 2*61 = 122
_________________
Kindly press "+1 Kudos" to appreciate
Manager
Joined: 20 Feb 2017
Posts: 162
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
Re: If both roots of the quadratic equation y^2 -63y +x =0 are prime numbe  [#permalink]

Show Tags

18 Mar 2019, 06:37
Sum of roots in a quadratic equation : (-b/a)
thus here sum of roots = 63
only one case would be possible that is 61+2 = 63 ( since 63 is odd , we need odd+even, hence only one condition is possible. 2 is only even prime number)
Hence the value of x = 61*2 =122
_________________
If you feel the post helped you then do send me the kudos (damn theya re more valuable than \$)
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: If both roots of the quadratic equation y^2 -63y +x =0 are prime numbe  [#permalink]

Show Tags

19 Mar 2019, 19:12
manpreetsingh86 wrote:
If both roots of the quadratic equation y^2 -63y +x =0 are prime numbers then number of possible value of x is

a) 0
b) 1
c) 2
d) 4
e) more than 4

We see that we need two values that sum to 63. Since 63 is odd and each root is prime, one of them must be 2 (the only even prime number). In that case, the other root is 61. So x = 2(61) = 122. That is, there is only one value possible for x.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: If both roots of the quadratic equation y^2 -63y +x =0 are prime numbe   [#permalink] 19 Mar 2019, 19:12
Display posts from previous: Sort by