The number 571+572+573 can be expressed as the products of 3

Question

The number 571+572+573 can be expressed as the products of 3 consecutive integers. What is the sum of these 3 consecutive integers?

A. 32
B. 33
C. 34
D. 35
E. 36

Bunuel · Accepted Answer

571+572+573 = 3*572 = 3*(2^2*11*13) = 11*12*13 --> 11+12+13 = 36.

Answer: E.

P.S. Please provide OA's for the questions.

mbaiseasy · Answer

=571+572+573=1716=(13)(11)(2)(2)(3)

after seeing 11 and 13, I knew the third should be 12 without calculating rem. factors.

=11+12+13= 36

Answer: E

PareshGmat · Answer

Addition of any 3 consecutive numbers is always divisible by 3

So, options A, C , D are ruled out

Now focus on options 33 & 36

It can be either

10, 11, 12 (Gives zero at the end after multiplication; ignore this series)

or

11, 12, 13 (Matches fine)

Answer = E

bhatiavai · Answer

571+572+573 = 1716 = 2*2*3*11*13 = 12*11*13

11+12+13 = 36

sanket1991 · Answer

571 + 572 + 573 can be written as 
572 -1 + 572 + 572 + 1 = 3*572 = 3 * 4 * 11 * 13 = 11 * 12 * 13... 
Ans. E

niks18 · Answer

571+572+573 = 1716

Now,  1716 = 11*12*13

So  11+12+13=36

Option  E

petrified17 · Answer

how did you derive 11*12*13 from 1716?

niks18 · Answer

Hi  petrified17

Factorize 1716, you will get 2*2*3*11*13. so it is evident that the three consecutive numbers has to be 11, 12 & 13

KarishmaB · Answer

Another method is to note that the sum of these three will end in 6.

If product of 3 consecutive integers ends in 6, the units digits of integers would be either 1, 2, 3 or 6, 7, 8.

The units digit of sum of the units digits 1, 2, 3 would be 6 giving only possible answer 36.
The units digit of sum of the units digits 6, 7, 8 would be 1 which is not there in the options.

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goobo · Answer

Another approach:

Sum of 3 consecutive integers is 3n + 3.

Subtracting 3 from each of the answer choices, we can eliminate A, C, D as they will not be divisible by 3. We are left with B and E.

B) 33 = 3n + 3 => n = 10 
E) 36 = 3n + 3 => n = 11

Since the sum of 571, 572 and 573 gives a unit digit of 6, n cannot be 10 so we can eliminate answer choice B.

We are left with answer choice E.

Tushar2804 · Answer

My take on this question was to focus on the last integer of the sum of the 3 numbers. It is 6. 
In all the options given, except E there is no other option that satisfies both the conditions - product of consecutive integers and also the units digits of the product being 6.

So yes, E is the only possible answer.

bumpbot · Answer

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The number 571+572+573 can be expressed as the products of 3

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