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

It is currently 16 Nov 2019, 16:52

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

If a and b are both factors of 50, which of the following must be true

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59086
If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 09 Sep 2019, 21:07
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

49% (01:41) correct 51% (01:34) wrong based on 106 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
avatar
P
Joined: 18 May 2019
Posts: 453
GMAT ToolKit User Premium Member CAT Tests
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 09 Sep 2019, 21:53
1
We are informed that a and b are factors of 50. We are to determine which of the answer choices must be true.
factors of 50 are {1,2,5,10,25,50}.
In A, we are given that ab≥2. This is not always true for the situation a=b=1, where ab=1.
In B, a+b≤50. This also not always true for the situation a=25, and b=50, whereby a+b=75.
In C, ab is factor of 100. This not always true for a=10 and b=25, where ab=250.
In E, ab is even. This is not necessary true for a=1, and b=5, where ab=5, which is not even.
In D, ab is a factor of 2500. This always true since taking the highest possible values that a and be can take, a=b=50, and computing ab=2500. In this case 2500 is a factor of 2500. Hence D must be true.

Answer is therefore D.
Senior Manager
Senior Manager
avatar
P
Joined: 07 Mar 2019
Posts: 381
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
CAT Tests
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 09 Sep 2019, 22:18
2
50 has total 6 factors – 1, 2, 5, 10, 25 and 50.

Since nothing is mentioned about relationship between ‘a’ and ‘b’ following conditions are possible:

a. a > b
b. a = b
c. a < b
where 1 ≤ a ≤ 50 and 1 ≤ b ≤ 50.

Let’s test by invalidating ‘must be true’ for all possible conditions –
Attachment:
File comment: 50 has total 6 factors –
50 has total 6 factors.JPG
50 has total 6 factors.JPG [ 75.65 KiB | Viewed 1042 times ]

* - Since 2500 has total 15 factors which include all the 6 factors of 50, taking possible extreme values of ‘a’ and ‘b’ is sufficient.

Answer (D).
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Senior Manager
Senior Manager
User avatar
P
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 383
GPA: 4
If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post Updated on: 10 Sep 2019, 23:13
1
If a and b are both factors of 50, which of the following must be true?

Factors of 50: 1, 2, 5, 10, 25 and 50

(A) ab≥ 2 - If a=1 and b=2, ab≥ 2 but if a=1 and b=1, then a<2.....no

(B) a + b≤ 50 - if a=50 and b=25, then no

(C) ab is a factor of 100. - if a=25 and b=10, then no

(D) ab is a factor of 2500. - if a=50 and b=25...yes ALWAYS

(E) ab is even. - if a=1 and b=5, then no

IMO answer is option D
_________________
Kudos OK Please!!

ALL ABOUT GMAT- \(https://exampal.com/gmat/blog/gmat-score-explained\)

Originally posted by EncounterGMAT on 09 Sep 2019, 22:28.
Last edited by EncounterGMAT on 10 Sep 2019, 23:13, edited 2 times in total.
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 777
Location: United States
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 10 Sep 2019, 04:09
1
Quote:
If a and b are both factors of 50, which of the following must be true?

(A) ab≥ 2
(B) a + b≤ 50
(C) ab is a factor of 100.
(D) ab is a factor of 2500.
(E) ab is even.


\(number.f(50)=(5^2,2)=(3)(2)=6\); and \(factors(50)=(1,50,2,25,5,10)\); \(a,b=any=(1,50,2,25,5,10)\)

(A) ab≥ 2: \(a,b=(1,1):ab=1\) false
(B) a + b≤ 50: \(a,b=(50,50):ab=2500\) false
(C) ab is a factor of 100: \(a,b=(50,25):ab=1250\) false
(E) ab is even: \(a,b=(1,1):ab=1\) false

Answer (D)
Senior Manager
Senior Manager
User avatar
G
Joined: 29 Jun 2019
Posts: 467
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 10 Sep 2019, 06:16
Factors of 50:2*5²
Factors of 2500:2²*5⁴
So, all factors of 50 are factors of 2500 too.
Option D

Posted from my mobile device
_________________
Always waiting
Intern
Intern
avatar
B
Joined: 18 Feb 2014
Posts: 1
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 10 Sep 2019, 06:25
Prime factorization results to: 50 = 10*5 = 5*2*5
Thus, factors are: 1, 2, 5, 10, 25, 50
What must be true is that ab >= 2 since smallest factors are 1 and 2.
So the correct answer should be A.
Manager
Manager
User avatar
G
Joined: 17 Jul 2014
Posts: 172
GMAT ToolKit User CAT Tests
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 10 Sep 2019, 10:19
If a and b are both factors of 50, which of the following must be true?

factors of 50 = 1, 2, 5, 10, 25, 50
some options were very easy to eliminate, the one that took time was A and D ...however, at the end , figured out

(A) ab≥ 2
a = 1, b = 1
1>=2 Not True

(B) a + b≤ 50
50+50 <= 50 -> Not true

(C) ab is a factor of 100
50*50 is not a factor of 100 -> Not true

(D) ab is a factor of 2500
50*50 is a factor of 2500 -> True
1*1 is a factor of 2500 -> True
2 * 25 is a factor of 2500 -> True

(E) ab is even
25 * 5 is not even -> Not true
1*5 is not even -> Not true

D is the answer!
VP
VP
avatar
D
Joined: 20 Jul 2017
Posts: 1073
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 10 Sep 2019, 11:37
Factors of 50 are {1, 2, 5, 10, 25, 50}
Note: a & b can take same values!

(A) ab≥ 2 —> NO [(a, b) = (1, 1)]
(B) a + b≤ 50 —> NO [(a,b) = (25, 50), (50, 50) etc.,]
(C) ab is a factor of 100. —> NO [(a, b) = (50, 50) etc.]
(D) ab is a factor of 2500. —> YES [Maximum value of ab = 50*50 = 2500, which is still a factor of 2500]
(E) ab is even. —> NO [(a, b) = (1, 1), (5, 25) etc.]

IMO Option D

Pls Hit kudos if you like the solution

Posted from my mobile device
SVP
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1843
Location: India
Premium Member Reviews Badge CAT Tests
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 10 Sep 2019, 23:32
Bunuel wrote:

Competition Mode Question



If a and b are both factors of 50, which of the following must be true?

(A) ab≥ 2
(B) a + b≤ 50
(C) ab is a factor of 100.
(D) ab is a factor of 2500.
(E) ab is even.


a is a factor of 50
b is a factor of 50
ab is a factor of 50*50 = 2500

IMO D
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8383
Location: United States (CA)
Re: If a and b are both factors of 50, which of the following must be true  [#permalink]

Show Tags

New post 17 Sep 2019, 09:49
1
Bunuel wrote:

Competition Mode Question



If a and b are both factors of 50, which of the following must be true?

(A) ab≥ 2
(B) a + b≤ 50
(C) ab is a factor of 100.
(D) ab is a factor of 2500.
(E) ab is even.


Since a is a factor of 50 and b is also a factor of 50, then ab is a factor of 50 x 50 = 2500.

To eliminate the other choices,consider the factors of 50: 1, 2, 5, 10, 25, and 50.
Choice A is incorrect because if a = 1 and b = 1, then ab = 1, and A is not true.
Choice B is incorrect because if a = 50 and b = 10, then a + b = 60 and B is not true.
Choice C is incorrect because if a = 25 and b = 10, then ab = 250, which is not a factor of 100.
Choice D is true because every product of two factors of 50 is also a factor of 50 x 50 = 2500.
Choice E is incorrect because if a = 1 and b = 5, then ab = 5, which is odd, so E is not true.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
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.

GMAT Club Bot
Re: If a and b are both factors of 50, which of the following must be true   [#permalink] 17 Sep 2019, 09:49
Display posts from previous: Sort by

If a and b are both factors of 50, which of the following must be true

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne