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twobagels
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Number 'abc', where a, b and c are distinct digits, is an even positiv 14 Sep 2020, 10:58
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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65% (02:34) correct 35% (01:58) wrong based on 182 sessions

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Number 'abc', where a, b and c are distinct digits, is an even positive integer that is a multiple of 33. abc is less than 300. If abc were one unit more, it would be a prime number. Which of the following are the correct values of a, b and c?

A) a=1, b=3, c=2
B) a=1, b=5, c=4
C) a=1, b=7, c=6
D) a=2, b=6, c=4
E) a=1, b=9, c=8

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E
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nick1816
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Number 'abc', where a, b and c are distinct digits, is an even positiv 14 Sep 2020, 11:08
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Eliminate A, B, C and D, as for those options 'abc'+1 is not a prime number.
133 is a multiple of 7, 177 is a multiple of 3 and 155 and 265 are multiples of 5.


E


twobagels
Number 'abc', where a, b and c are distinct digits, is an even positive integer that is a multiple of 33. abc is less than 300. If abc were one unit more, it would be a prime number. Which of the following are the correct values of a, b and c?

A) a=1, b=3, c=2
B) a=1, b=5, c=4
C) a=1, b=7, c=6
D) a=2, b=6, c=4
E) a=1, b=9, c=8

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Number 'abc', where a, b and c are distinct digits, is an even positiv 14 Sep 2020, 11:38
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Nicely eliminated Nick :)
I did it a long way.. I wrote all multiples of 33 less than 300. It was like writing table of 33 :)
Multiples of 33 less than 300 are 33, 66, 99, 132, 165, 198, 231, 264, 297
since abc is a three digit even number, we are left with 132, 198, 264

+1 to all the above number = 133, 199, 265.. One of these is a prime number as per the question.
133 is divisible by 7 and 265 is divisible by 5. So, the selected prime number is 199. Corresponding number is 198

hence, E
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Number 'abc', where a, b and c are distinct digits, is an even positiv 09 Oct 2020, 12:16
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I eliminated the options ending in 4 as 4+1 is 5. Then, I eliminated the option C as it is not multiple of 3. That left me with E and A. I checked C+1 for 7 which came out to be a factor of 133 (132+1). So E is the right answer.
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Number 'abc', where a, b and c are distinct digits, is an even positiv 10 Oct 2020, 08:13
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Prime numbers are above 3 are generally 6k+1 or 6k-1
So check 33 x 6= 198 .. 6(33)+1 = 199 ... this is prime
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Number 'abc', where a, b and c are distinct digits, is an even positiv Updated on: 12 Oct 2020, 10:41
Originally posted by Kapidhwaj on 11 Oct 2020, 04:21.
Last edited by Kapidhwaj on 12 Oct 2020, 10:41, edited 1 time in total.
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rsrighosh
Prime numbers are above 3 are generally 6k+1 or 6k-1
So check 33 x 6= 198 .. 6(33)+1 = 199 ... this is prime
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All numbers in options except C (correction: and B) are multiples of 6. Also, question stem says even multiples of 33, so these would be in form of 6k.
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Number 'abc', where a, b and c are distinct digits, is an even positiv Updated on: 16 Oct 2020, 01:09
Originally posted by MathRevolution on 11 Oct 2020, 14:08.
Last edited by MathRevolution on 16 Oct 2020, 01:09, edited 1 time in total.
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Condition1: Multiple of 33

=> 33 = 3 * 11

The number 'abc' should be divisible by both '3' and '11'.

Option A: 132 - Divisible by '3' and '11'
Option B: 154 - Not divisible by '3'
Option C: 176 - Not divisible by '3'

Option D: 264 - Divisible by '3' and '11'
Option E: 198 - Divisible by '3' and '11'

Condition 2: abc + 1 is a prime number

Option A: 132 - 132 + 1 = 133 is divisible by '7' and hence it is not a prime number

Option D: 264 - 264 + 1 = 265 is divisible by '5' and hence it is not a prime number

Option E: 198 - 198 + 1 = 199 - It is a prime number

Answer E
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Number 'abc', where a, b and c are distinct digits, is an even positiv 16 Oct 2020, 00:16
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there are only 3 Possibilities in which the Value is a 3 DIGIT - EVEN Multiple of 33 that is Less Than < 300


33 * (4) = 132

or

33 * (6) = 198

or

33 * (8) = 264



Adding +1 to the 3 Digit Number will make it Prime:

264 + 1 = 265 is definitely out



132 + 1 = 133

Multiplication Table of 19 up through 10s:
....
19 * 5 = 95

19 * 6 = 114

19 * 7 = 133

thus, 132 is out


The Correct Number must be 198

a = 1
b=9
c=8

-E-
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Number 'abc', where a, b and c are distinct digits, is an even positiv 23 Oct 2020, 05:52
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Write out the even multiples of 33: 66, 132, 198, 264

If abc were on unit more, it would be a prime number. Which of the following are correct values of a, b, and c?

Eliminate B and D right away because if we add 1 the number would end in a 5, which would not give us a prime number. Eliminate C because it's not a multiple of 33. We're left with A and E.

A) 132 + 1 = 133
E) 198 + 1 = 199

E is clearly prime so it is the answer. If you started with A, a quick way to check if it's divisible by 7 is to take the last digit and double it. Then subtract the last digit from the other digits. If the resulting number is divisible by 7, then it is a multiple of 7.

133

13 and 6

13 - 7 = 7

Therefore, A is not prime. Answer is E.
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