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

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tinashine20
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The number 571+572+573 can be expressed as the products of 3 [#permalink] New post   Updated on: 25 Mar 2014, 02:08
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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
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E

Originally posted by tinashine20 on 26 Nov 2012, 05:03.
Last edited by Bunuel on 25 Mar 2014, 02:08, edited 1 time in total.
Added the OA.
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Re: The number 571+572+573 cab be expressed [#permalink] New post   26 Nov 2012, 05:19
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tinashine20 wrote:
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


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.
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Re: The number 571+572+573 can be expressed as the products of 3 [#permalink] New post   20 Dec 2012, 00:37
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tinashine20 wrote:
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


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

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

\(=11+12+13= 36\)

Answer: E
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Re: The number 571+572+573 can be expressed as the products of 3 [#permalink] New post   25 Mar 2014, 01:46
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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
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Re: The number 571+572+573 can be expressed as the products of 3 [#permalink] New post   24 Dec 2014, 06:33
571+572+573 = 1716 = 2*2*3*11*13 = 12*11*13

11+12+13 = 36
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Re: The number 571+572+573 can be expressed as the products of 3 [#permalink] New post   25 Dec 2014, 00:05
571 + 572 + 573 can be written as
572 -1 + 572 + 572 + 1 = 3*572 = 3 * 4 * 11 * 13 = 11 * 12 * 13...
Ans. E
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Re: The product of three consecutive integers is equal to 571+572+573. [#permalink] New post   20 Sep 2017, 00:27
petrified17 wrote:
:roll: The product of three consecutive integers is equal to 571+572+573.
What is the sum of thoseconsecutive integers?

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


\(571+572+573 = 1716\)

Now, \(1716 = 11*12*13\)

So \(11+12+13=36\)

Option \(E\)
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Re: The product of three consecutive integers is equal to 571+572+573. [#permalink] New post   20 Sep 2017, 00:29
niks18 wrote:
petrified17 wrote:
:roll: The product of three consecutive integers is equal to 571+572+573.
What is the sum of thoseconsecutive integers?

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


\(571+572+573 = 1716\)

Now, \(1716 = 11*12*13\)

So \(11+12+13=36\)

Option \(E\)


how did you derive 11*12*13 from 1716?
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Re: The product of three consecutive integers is equal to 571+572+573. [#permalink] New post   20 Sep 2017, 00:42
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petrified17 wrote:
niks18 wrote:
petrified17 wrote:
:roll: The product of three consecutive integers is equal to 571+572+573.
What is the sum of thoseconsecutive integers?

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


\(571+572+573 = 1716\)

Now, \(1716 = 11*12*13\)

So \(11+12+13=36\)

Option \(E\)


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


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
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Re: The number 571+572+573 can be expressed as the products of 3 [#permalink] New post   20 Sep 2017, 03:01
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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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The number 571+572+573 can be expressed as the products of 3 [#permalink] New post   03 Dec 2018, 22:23
tinashine20 wrote:
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


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.
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