If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is : Problem Solving (PS)

My Profile Logout

Test's Subscription Expires:

My Follow Feed Kudos My Error Log

Messages and Replies

Settings Mark All Read

See All

Applicant Notifications

Settings Mark All Read

See All

Global notifications

Settings Mark All Read

See All

If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is

Sort by Date

Sort by Kudos

Author

Message

TAGS:

Hide Tags

Math Expert

Joined: 02 Aug 2009

Posts: 7199

If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

Show Tags

25 Dec 2017, 21:39

00:00

Difficulty:

65% (hard)

Question Stats:

42% (01:03) correct

58% (01:04) wrong

based on 91 sessions

HideShow timer Statistics

If \(10 \leq x \leq 20\) and \(5 \leq y \leq 10\), and xy is a prime number, what is the least possible value of xy?

(A) 2
(B) 11
(C) 53
(D) 77
(E) Not possible

New Question

Spoiler: OA

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern

Joined: 25 Dec 2017

Posts: 6

Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

Show Tags

25 Dec 2017, 21:59

Interesting question. I don’t understand how xy can be a prime number as the very fact that the number is formed by multiplying x and y precludes it from being a prime number unless I’m reading the question wrongly.

Sent from my iPhone using GMAT Club Forum

Math Expert

Joined: 02 Aug 2009

Posts: 7199

Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

Show Tags

25 Dec 2017, 22:07

szeth wrote:

Hi..

It is nowhere mentioned x and y are integers..
I was about to add " not possible" as a choice, ill do it now
_________________

Current Student

Joined: 14 Jun 2017

Posts: 22

Location: United States

Schools: Kellogg PT '21 (A), Booth PT '21 (M)

GMAT 1: 710 Q48 V38

GPA: 2.8

If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

Show Tags

Updated on: 26 Dec 2017, 00:53

chetan2u , I am new to the forums. How can I retain format of algebraic formulae in my posts? Thanks. BTW- I've read a lot of your posts. You're an awesome teacher and your explanations have helped me learn a lot!

Since \(10 <= x <= 20\) and \(5 <= y <= 10\),

50<=xy<=200.

Now xy is a prime number- no way to get 2, no way to get 11 either. We can get 53 by taking y=5.3 and x=10. So least value of xy is 53. Hence C. Please confirm.

Originally posted by Tranquil Focus on 25 Dec 2017, 22:29.
Last edited by Tranquil Focus on 26 Dec 2017, 00:53, edited 2 times in total.

Intern

Joined: 25 Dec 2017

Posts: 6

Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

Show Tags

25 Dec 2017, 22:29

Ah fair enough.

@tranquil focus your method seems to make sense. I do not know how to give kudos via my phone but thanks for solving this

Sent from my iPhone using GMAT Club Forum

Math Expert

Joined: 02 Sep 2009

Posts: 52168

Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

Show Tags

26 Dec 2017, 00:26

Tranquil Focus wrote:

chetan2u , I am new to the forums. How can I retain format of algebraic formulae in my posts?

Writing Mathematical Formulas on the Forum: https://gmatclub.com/forum/rules-for-po ... l#p1096628
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager

Joined: 24 Nov 2016

Posts: 152

Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

Show Tags

28 Dec 2017, 04:45

chetan2u wrote:

If \(10 \leq x \leq 20\) and \(5 \leq y \leq 10\), and xy is a prime number, what is the least possible value of xy?

(A) 2
(B) 11
(C) 53
(D) 77
(E) Not possible

A prime has 2 factors, {1,itself}. The stem doesn't say that x or y are integers.. thus, we can make a prime number multiplying with decimals.

The least possible value for xy = prime, has to be the first prime after the lower range \(5*10=50\), which is \(53=10*5.3\) (10 is x and 5.3 is y).

(C) is the answer.