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

It is currently 15 Dec 2018, 09:11

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

How many three-digit numbers contain three primes that sum to an even

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
How many three-digit numbers contain three primes that sum to an even  [#permalink]

Show Tags

New post 19 Jul 2017, 22:50
1
14
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (01:39) correct 59% (02:18) wrong based on 196 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7107
How many three-digit numbers contain three primes that sum to an even  [#permalink]

Show Tags

New post 24 Jul 2017, 19:06
3
1
Bunuel wrote:
How many three-digit numbers contain three primes that sum to an even number?

A. 27
B. 28
C. 54
D. 55
E. 64



Hi,
if you dont want to calculate separately..

Ways the sum will be ODD is if
    # all 3 are even or
    # one is even and remaining 2 are odd
I. 1 even and other 2 odd
let the first number be 2, the remaining 2 can be filled with any of the 3,5,7.., so 2,_,_ thus 1*3*3
Now 2 can be placed in ANY of three position, that is 2,_,_ or _,2_ or _,_,2, so 1*3*3*3=27..
II. all even
ofcourse a number without any odd prime 222..

so \(27+1=28\)

B
_________________

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

Most Helpful Community Reply
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1376
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: How many three-digit numbers contain three primes that sum to an even  [#permalink]

Show Tags

New post 19 Jul 2017, 23:20
5
Bunuel wrote:
How many three-digit numbers contain three primes that sum to an even number?

A. 27
B. 28
C. 54
D. 55
E. 64


There are 4 prime digit numbers: 2, 3, 5, 7.

Since sum of 3 primes is an even number, all of them are even, or one of them is 2 and others isn't 2.

Case 1. Three digit numbers are different.

We must select 2 first. Now, we need to select 2 others from set {3, 5, 7}. We have 3C2 = 3 possible ways to select.

Now, with 3 different digits, we could create 3 * 2 * 1 = 6 different three-digit numbers from each set of 3 different digits.

Hence, we could totally create 6 * 3 = 18 different three-digit numbers.

Case 2. First digit is 2 and two others are identical.

We simply select a number from set {3, 5, 7}. There are 3 possible ways to select it.

Now, from each set of 2 and two other identical numbers, we could create 3 * 2 * 1 / 2 = 3 different three-digit numbers.

Hence, we could totally create 3 * 3 = 9 different three-digit numbers.

Case 3. All of 3 digits are identical.

In this case, we could create only one number 222.

Hence, the result of this question is: 18 + 9 + 1 = 28.

The answer is B
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

General Discussion
Manager
Manager
avatar
B
Joined: 13 Apr 2017
Posts: 84
Location: India
Concentration: General Management, International Business
GMAT 1: 660 Q40 V41
GPA: 3.4
WE: Engineering (Energy and Utilities)
Re: How many three-digit numbers contain three primes that sum to an even  [#permalink]

Show Tags

New post 24 Jul 2017, 18:57
1
Bunuel wrote:
How many three-digit numbers contain three primes that sum to an even number?

A. 27
B. 28
C. 54
D. 55
E. 64


The four single digit prime numbers are 2,3,5 and 7.
a) If we take these numbers in groups of 3s (remember the sum should be even) :
1) 2,3,5 - 6 possible numbers
2) 2,5,7 - 6 possible numbers
3) 2,3,7 - 6 possible numbers
All the above combinations will give even numbers upon adding the three digits of the number.
Hence total 6 * 3 = 18 possibilities.

b) Now since we need '2' to be present out of the three digits to keep the sum even, keep '2' and repeat the remaining primes, i.e. 233, 255, 277
Each of these three numbers can be presented in 3 ways.
Now total possibilities = 18 + 9 = 27

c) Moreover 222 will also give an even number when the digits are summed up.
Therefore total possibilities = 27+1 = 28

Answer : B
Manager
Manager
avatar
B
Joined: 13 Apr 2017
Posts: 84
Location: India
Concentration: General Management, International Business
GMAT 1: 660 Q40 V41
GPA: 3.4
WE: Engineering (Energy and Utilities)
Re: How many three-digit numbers contain three primes that sum to an even  [#permalink]

Show Tags

New post 26 Jul 2017, 20:45
chetan2u wrote:
Bunuel wrote:
How many three-digit numbers contain three primes that sum to an even number?

A. 27
B. 28
C. 54
D. 55
E. 64



Hi,
if you dont want to calculate separately..

let the first number be 2, the remaining 2 can be filled with any of the 3,5,7..
so 1*3*3
this 1, that is 2, can be placed in of three position so 1*3*3*3=27..

ofcourse a number without any odd prime 222..

so 27+1=28

B


Much easier approach. Thanks Chetan.
Intern
Intern
avatar
B
Joined: 26 Jan 2018
Posts: 1
How many three-digit numbers contain three primes that sum to an even  [#permalink]

Show Tags

New post 27 Oct 2018, 04:51
chetan2u wrote:
Bunuel wrote:
How many three-digit numbers contain three primes that sum to an even number?

A. 27
B. 28
C. 54
D. 55
E. 64



Hi,
if you dont want to calculate separately..

Ways the sum will be ODD is if
    # all 3 are even or
    # one is even and remaining 2 are odd
I. 1 even and other 2 odd
let the first number be 2, the remaining 2 can be filled with any of the 3,5,7.., so 2,_,_ thus 1*3*3
Now 2 can be placed in ANY of three position, that is 2,_,_ or _,2_ or _,_,2, so 1*3*3*3=27..[/color]
II. all even
ofcourse a number without any odd prime 222..

so \(27+1=28\)

B


Hi Chetan,

This is really helpful. Just one question - Since we're trying to re-arrange 3 integers - why shouldn't this be multiplied by 3! instead of 3?
GMAT Club Bot
How many three-digit numbers contain three primes that sum to an even &nbs [#permalink] 27 Oct 2018, 04:51
Display posts from previous: Sort by

How many three-digit numbers contain three primes that sum to an even

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.