GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 24 Feb 2020, 04:45

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 integers with each being greater than 1, is ab > 20?

  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: 61441
If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 22 Jan 2020, 23:11
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:32) correct 38% (01:46) wrong based on 65 sessions

HideShow timer Statistics

VP
VP
avatar
V
Joined: 20 Jul 2017
Posts: 1330
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 22 Jan 2020, 23:28
3
If a and b are integers with each being greater than 1, is ab > 20?

Possible values of a or b = 2, 3, 4, 5, . . . . . . .

(1) a + b = 9
--> Possible values of (a, b):
1. (a, b) = (2, 7) or (7, 2) --> Product = 2*7 = 14
2. (a, b) = (3, 6) or (6, 3) --> Product = 3*6 = 18
3. (a, b) = (4, 5) or (5, 4) --> Product = 4*5 = 20

So, the product is NEVER greater than 20 --> Sufficient

(2) (a − 4)^2 + (b − 5)^2 = 0
--> Only possible when (a - 4)^2 = 0 & (b - 5)^2 = 0
--> a = 4 & b = 5
--> Product = a*b = 4*5 = 20
Not greater than 20 --> Sufficient

Option D
Director
Director
avatar
V
Joined: 30 Sep 2017
Posts: 674
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post Updated on: 23 Jan 2020, 03:52
1
Integers a>1 and b>1. Is ab > 20?

(1) a + b = 9
a=1, b=8, ab<=20
a=4, b=5, ab<=20
SUFFICIENT

(2) (a − 4)^2 + (b − 5)^2 = 0
The only possible solution is (a,b) =(4,5). ab<=20
SUFFICIENT.

FINAL ANSWER IS (D)

Posted from my mobile device

Originally posted by chondro48 on 22 Jan 2020, 23:31.
Last edited by chondro48 on 23 Jan 2020, 03:52, edited 1 time in total.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3186
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge CAT Tests
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 22 Jan 2020, 23:54
1
Quote:
If a and b are integers with each being greater than 1, is ab > 20?

(1) a + b = 9

(2) (a − 4)^2 + (b − 5)^2 = 0


Given: a and b are integers with each being greater than 1

Question: is ab > 20?

Statement 1: a + b = 9

CONCEPT: For given addition of two (or more) values the product of those values is maximum when they are equally distributed. E.g. for a+b=10, \((a*b)_{max}= 5*5 = 25\)

Similarly for \((a*b)_{max}\), a=4 and b = 5 (cause they are integers)
i.e. \((a*b)_{max}= 5*4 = 20\)

i.e. a*b can NOT be greater than 20 (Unique and consistent answer) hence

SUFFICIENT

Statement 2: \((a − 4)^2 + (b − 5)^2 = 0\)

Since square of any value can't be less than 0 therefore each (a-4)^2 and (b-5)^2 must be zero
i.e. a=4 and b=5
i.e. \((a*b)_{max}= 5*4 = 20\)

i.e. a*b can NOT be greater than 20 (Unique and consistent answer) hence

SUFFICIENT

Answer: Option D
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

Click here for Our VERBAL & QUANT private tutoring package details

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Manager
Manager
User avatar
P
Joined: 27 Feb 2017
Posts: 235
Location: United States (WA)
GMAT 1: 760 Q50 V42
GRE 1: Q169 V168
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 01:05
1
The answer is (D).
(1) a + b = 9
Because
a = 2, b = 7, and ab = 14
a = 3, b = 6, and ab = 18
a = 4, b = 5, and ab = 20
...
If ab > 20? The answer is definitive No. SUFFICIENT.

(2) (a − 4)^2 + (b − 5)^2 = 0
a = 4, b = 5, and ab =20.
If ab > 20? The answer is definitive No. SUFFICIENT.

So, we choose "D".


(I have to admit that I made the mistake of choosing B at first. )
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5906
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 01:39
#1
a + b = 9
a,b = 4,5 or any other value 7,2; 8,1 ; 3,6 ;
ab>20 not possible
sufficient
#2
a,b = 4,5
sufficient
IMO D
(a − 4)^2 + (b − 5)^2 = 0
possible w

If a and b are integers with each being greater than 1, is ab > 20?

(1) a + b = 9

(2) (a − 4)^2 + (b − 5)^2 = 0
Senior Manager
Senior Manager
User avatar
D
Joined: 20 Mar 2018
Posts: 468
Location: Ghana
Concentration: Finance, Real Estate
Reviews Badge
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 02:57
1
If a and b are integers with each being greater than 1, is ab > 20?

Constraint: a=Integer >1 ~ +ve int.
b=Integer >1 ~ +ve int.
Asked: Is ab > 20 Yep! Or ab < = 20 Nope!

(1) a + b = 9
When a = 4 ,b=5
a•b =20 so Nope! ab = 20
When a= 3,b= 6
a•b = 18 so Nope! ab < 20
We keep getting Nope! So
(Sufficient)

(2) (a − 4)^2 + (b − 5)^2 = 0
When a= 4 ,b= 5
(4-4)^2 + (5-5)^2 = 0
Any other value of a and b won’t satisfy the equation
Here a•b = 20 so Nope a•b ain’t greater than 20
(Sufficient)

Hit that D
Posted from my mobile device
Intern
Intern
avatar
B
Joined: 28 Jan 2019
Posts: 44
GMAT 1: 480 Q48 V14
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 03:33
Max value of a + b = 9 is when a equals to b....4.5 and 4.5 therefore ( 4.5 * 4.5) is 20.25 i.e greater than 20 but a and b can be 1 and 8 also so less than 20....


So insufficient....


Whereas in 2nd statement ..... A sum of square is zero when a = 4 and b= 5..... Therefore a*b is 20 ....so we get the answer...

B is sufficient

Posted from my mobile device
CrackVerbal Quant Expert
User avatar
G
Joined: 12 Apr 2019
Posts: 385
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 03:54
1
From the question statement we understand that both a and b belong to the following set:
{2,3,4,5,6,…..}. We are to find out if the product of ab is greater than 20. Since this is a YES-NO type of DS question, we need to obtain a deifinite YES or a definite NO as an answer.

From statement I alone, a+b = 9. Since neither a nor b can be equal to 1, the only combinations that satisfy the above equation will be (5,4), (6,3) and (7,2).

For each of these combinations, the product is either equal to 20 or less than 20.
Is ab>20? Clearly, NO. Statement I alone is sufficient.

Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, \((a-4)^2\) + \((b-5)^2\) = 0.
Remember that the square of any number is always a NON-NEGATIVE value. This means that the square of a number can be either ZERO or POSITIVE, it will never be negative.

In the equation given, we have two squares being added to give us ZERO. This can happen only if both the squares are ZERO themselves i.e. \((a-4)^2\) = 0 and \((b-5)^2\) = 0. As per this, a = 4 and b = 5.

Using these values of a and b, ab = 20. Is ab>20? Clearly, the answer is a NO again.
Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

Hope that helps!
_________________
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1224
Location: United States
CAT Tests
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 05:28
1
Quote:

If a and b are integers with each being greater than 1, is ab > 20?

(1) a + b = 9

(2) (a − 4)^2 + (b − 5)^2 = 0


(a,b)>1=ie.(2,2)

(1) a + b = 9 sufic

a+b=9; max(a,b)=(4,5)=20, min=()=9, ans=no

(2) (a − 4)^2 + (b − 5)^2 = 0 sufic

\((a-4)^2…and…(b-5)^2≥0…(a,b)=(4,5)≤20\)

Ans (D)
Intern
Intern
avatar
S
Joined: 13 Nov 2019
Posts: 33
Concentration: Finance, Marketing
Schools: Darden '22
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 10:26
1
I think D shoukd be answer, as both are sufficient to answer the question.
First statement, highest product can go upto 20.
Second statement, also has the only product of 20.

Posted from my mobile device
Director
Director
avatar
P
Joined: 25 Jul 2018
Posts: 565
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 15:29
1
a,b --integers (a >1, b>1)
is ab >20 ???

(Statement1): a + b = 9
--> the maximum value of (a,b) pairs from (1,8),(2,7),(3,6),(4,5) is ( 4,5 )
ab =20 --> (Cannot be greater than 20-NO)
Sufficient

(Statement2): \((a − 4)^2 + (b − 5)^2 = 0\)
--> In order \((a − 4)^2 + (b − 5)^2\) to be equal to zero, \((a − 4)^2=0\) and \((b − 5)^2=0\) at the same time.
--> a=4, b =5
ab= 4*5=20
(Cannot be greater than 20-NO)
Sufficient

The answer is D.
Director
Director
User avatar
V
Joined: 28 Jul 2016
Posts: 875
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE: Project Management (Investment Banking)
Reviews Badge
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 19:01
1
given a and b each greater than 1

1) a+b= 9
now product is maximun when numbers are equal
hence nearest integers will be
4 and 5
their prod = 20
thus product will be <= 20
sufficient

(2) (a − 4)^2 + (b − 5)^2 = 0

or (a − 4)^2 = 0
thus a = 4
(b − 5)^2 = 0

or b = 5
product = 20
not greater
thus sufficient

hence D
_________________

Keep it simple. Keep it blank
Director
Director
User avatar
P
Joined: 16 Jan 2019
Posts: 573
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 19:24
1
(1) a + b = 9

Consider all possible pairs (2,7) (3,6) (4,5)

ab is never greater than 20

1 is sufficient

(2) (a − 4)^2 + (b − 5)^2 = 0

Sum of two perfect squares is 0. Since a square cannot be negative, the only possibility is that a=4 and b=5 and so ab=20

2 is sufficient

Answer is D

Posted from my mobile device
CR Forum Moderator
avatar
P
Joined: 18 May 2019
Posts: 712
GMAT ToolKit User Premium Member CAT Tests
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 19:45
1
We know that a and b are integers greater than 1. We are to determine if ab>20.

Statement 1: a+b=9
possible pairs are a=2, b=7 or b=2 and a=7, ab=14 !> 20 No.
a=3, b=6, or b=3, and a=6, ab=18 !> 20 No.
a=4, b=5 or a=5 and b=4, ab=20 !>0 No.
Statement 1 is sufficient.

Statement 2: (a-4)^2 + (b-5)^2 = 0
The square of a number is always a positive number or zero, hence the only way to get (a-4)^2 + (b-5)^2 = 0 is when a-4=0 and b-5=0, implying a=4 and b=5.
So ab=20 and 20 !>20 so statement 2 is also sufficient.

The answer is D.
Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 443
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Reviews Badge
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 21:25
1
Both are sufficient individually

a) all the below possibilities satisfies the condition
1,8
2,7
3,6
4,5
Sufficient

b)only possible solution is a=4,b=5...... sufficient

OA:D

Posted from my mobile device
Manager
Manager
avatar
G
Joined: 30 Jul 2019
Posts: 101
Location: Viet Nam
Concentration: Technology, Entrepreneurship
GPA: 2.79
WE: Education (Non-Profit and Government)
Re: If a and b are integers with each being greater than 1, is ab > 20?  [#permalink]

Show Tags

New post 23 Jan 2020, 22:38
1
Quote:
If a and b are integers with each being greater than 1, is ab > 20?

(1) a + b = 9

(2) \((a − 4)^2 + (b − 5)^2 = 0\)


Statement (1)
2*7=14
3*6 = 18
4*5 = 20
=> \(ab\leq{20}\)
=> Suff
Statement (2)
\((a − 4)^2 + (b − 5)^2 = 0\)
=> \(=> a = 4; b=5 => ab =20\)
=> Suff
=> Choice D
GMAT Club Bot
Re: If a and b are integers with each being greater than 1, is ab > 20?   [#permalink] 23 Jan 2020, 22:38
Display posts from previous: Sort by

If a and b are integers with each being greater than 1, is ab > 20?

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





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