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# Magoosh Brain Twister: A Prime Location

Ready for this week’s brain twisting math challenge question?

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

1. 27
2. 28
3. 54
4. 55
5. 64

Be sure to check back on Thursday for the answer and explanation! Good luck. ðŸ™‚

### 25 Responses to Magoosh Brain Twister: A Prime Location

1. shayan October 23, 2014 at 3:13 pm #

It is easy man.

Prime number which are lesser than 10: 2, 3, 5, 7
Even number=2
Odd Numbers=3, 5, 7

and we know that:

Odd+Odd+Odd=Even —————> 3*3*3=27
Even+Even+Even=Even————->1 (when our number is 222)
Even+Odd+Odd=Even—————>1*3*3=9
Odd+Even+Odd=Even—————>3*1*3=9
Odd+Odd+Even=Even—————>3*3*1=9

So 27+1+9+9+9=55

Therefore answer is D

• Chris Lele October 24, 2014 at 5:03 pm #

I think you double counted some cases (332, etc.).

2. tan October 23, 2014 at 9:02 am #

28

• Chris Lele October 24, 2014 at 5:02 pm #

That’s it!

3. Anusha October 23, 2014 at 4:34 am #

B.28

• Chris Lele October 24, 2014 at 5:04 pm #

That’s right!

4. edouard October 23, 2014 at 1:46 am #

Answer is B: 28.
There are 4 possible prime numbers including the only even (E) prime number 2 and the odd (O) prime numbers 3, 5, and 7. Let the 3-digit number be XYZ. X+Y+Z is even in four possible cases:
1) XYZ is EOO, thus there are 1*3*3=9 possible numbers
2) XYZ is EEE, thus it is the number 222
3) XYZ is OOE, thus there are 3*3*1=9 possible numbers
4) XYZ is OEO, thus there are 3*1*3=9 possible numbers
In total, there 9*3+1=28 possible numbers.

• Chris Lele October 24, 2014 at 5:04 pm #

Good explanation! That’s the answer ðŸ™‚

5. Hitesh October 23, 2014 at 12:24 am #

28

• Chris Lele October 24, 2014 at 5:07 pm #

That’s it!

6. Sanjay October 23, 2014 at 12:10 am #

_ _ _ : Three digit number to be filled by prime numbers such that they add up to an even number.

Case 1: Hundred’s place has 2
The tens place can be filled by any of the four prime numbers and similarly the units place.
So, total three digit nos in this case is 1 X 4 X 4 = 16

Case 2: Hundred’s place has 3
So any of the tens or units has to be occupied by 2 and other place can be occupied by any of the four primes. Sp total nos: 1 X 1 X 4=4

Similarly case 3 has 5 in hundreds place and case 4 has 7 in hundreds place and rest follows similar to case 2.

So, total nos of three digit numbers is 16 + 4 + 4 + 4 = 28

And the answer is B: 28

• Chris Lele October 24, 2014 at 5:08 pm #

Great explanation!

7. Ram October 22, 2014 at 9:09 pm #

28.
The numbers have to be EOO,OEE,OOE, EEE (Even/Odd). With 2,3,5,7 primes, first gives 9 choices, 2nd gives 9 choices, 3rd gives 9 choices and 4th gives 1. Total 28

• Chris Lele October 24, 2014 at 5:07 pm #

That’s it ðŸ™‚

8. Balaji October 22, 2014 at 8:34 pm #

Well from the above comments all of them have come up with answer but forgot the same prime number (3,5,7) can repeat twice for the 3 digit number. 2 can repeat only once i.e 222 . So answer will be total possibilities – number possible with two 2s.

64( 4*4*4) – 9 ( 3+3+3 ). = 54. Answer is 54

• Chris Lele October 24, 2014 at 5:07 pm #

I think you double counted some cases (332, 552, etc.)

9. Peach October 20, 2014 at 8:42 pm #

27..

• Chris Lele October 24, 2014 at 5:06 pm #

One off…I think you forgot 222.

10. Sirforgetsalot October 20, 2014 at 3:20 pm #

A.27

• Sirforgetsalot October 20, 2014 at 3:22 pm #

Sorry 28 :p

• Chris Lele October 24, 2014 at 5:06 pm #

Yep, that’s the right one ðŸ™‚

11. Akid October 20, 2014 at 10:45 am #

Hmm. I am not sure whether I understood this question clearly. Here’s my thought:
So among the 10 digits from 0-9 there are 4 digits which are prime (2,3,5,7) which will give us a total of 64 different numbers with these digits (2,3,5,7). However, the question requires the sum of the digits to be even. Therefore, there are only two possibilities: 1) All the numbers must be even or 2) 1 even number must be followed by 2 odds. According to option 1, we can get the number 222 where the individual digits add up to 6. As for option no. 2, 2 must be present in the number along with 2 odd prime numbers. If we plug in 2 at the hundreds place we get a total of 3*3 = 9 possibilities. Since our number is 3 digits the number of possibilities will be 3*9 = 27. Hence, the answer should be 27+1 = 28, i.e. B

• Chris Lele October 24, 2014 at 5:05 pm #

Got it–and a great explanation to boot!

12. zek October 20, 2014 at 9:56 am #

28

• Chris Lele October 24, 2014 at 5:05 pm #

That’s it!

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