If {x} is the product of all integer multiples of 5 from 1 to x, inclu

Question

If {x} is the product of all integer multiples of 5 from 1 to x, inclusive, what is the greatest prime number, y, such that ({36} + {41})/y is an integer?

A. 5
B. 11
C. 19
D. 23
E. 41

Luckisnoexcuse · Answer

{36} = 5*10*15*20*25*30*35 = 5^7 (7!)
{41} = 5*10*15*20*25*30*35*40 = 5^8 (8!)

({36} + {41}) = 5^7 (7!) (1+8*5) = 5^7 (7!) (41)

E

rajudantuluri · Answer

{x} is the product of all integer multiples of 5 from 1 to x.

So {36} = 5*10*15*20*25*30*35
So {41} = 5*10*15*20*25*30*35*40

{36} + {41} = (5*10*15*20*25*30*35) + (5*10*15*20*25*30*35*40)
 = (5*10*15*20*25*30*35) (1 + 40)
 = (5*10*15*20*25*30*35) * 41

Question asks us what is the greatest prime number, y, such that ({36} + {41})/y is an integer?

(5*10*15*20*25*30*35) * 41 --> 41 is the greatest prime number y can be so that the ({36} + {41})/y is still an integer

ScottTargetTestPrep · Answer

Let’s simplify {36} and {41}:

{36} = 5 x 10 x 15 x 20 x 25 x 30 x 35

{41} = 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40

Thus:

{36} + {41} = (5 x 10 x 15 x 20 x 25 x 30 x 35) + (5 x 10 x 15 x 20 x 25 x 30 x 35 x 40)

{36} + {41} = 5 x 10 x 15 x 20 x 25 x 30 x 35 x (1 + 40)

{36} + {41} = 5 x 10 x 15 x 20 x 25 x 30 x 35 x 41

Thus, the largest prime that will divide the above expression is 41.

Answer: E

lor12345 · Answer

Hi!
I didn't understand that solution. Can anybody help me with that?
I can understand the following, but the rest I dont!
{36} = 5 x 10 x 15 x 20 x 25 x 30 x 35
{41} = 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40
{36} + {41} = (5 x 10 x 15 x 20 x 25 x 30 x 35) + (5 x 10 x 15 x 20 x 25 x 30 x 35 x 40)
Thank you in ahead!

Bunuel · Answer

{36} + {41} = ( 5 x 10 x 15 x 20 x 25 x 30 x 35 ) + ( 5 x 10 x 15 x 20 x 25 x 30 x 35  x 40)

Factor out common part which is  5 x 10 x 15 x 20 x 25 x 30 x 35  to get 5 x 10 x 15 x 20 x 25 x 30 x 35 x (1 + 40);

5 x (2 x 5) x (3 x 5) x (2^2 x 5) x (5^2) x (2 x 3 x 5) x (5 x 7) x  41 .

The largest prime that will divide the above expression is 41.

Answer: E.

Hope it's clear.

lor12345 · Answer

Thank you! Yes, now it's clear!

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=qXLpPLSRDvQ

{36} = Product of all integer multiples of 5 from 1 to 36, inclusive 
=> {36} = 5 * 10 * 15 * ... * 35

Similarly, {41} = 5 * 10 * ... * 35 * 40

=>  {36} + {41}  = 5 * 10 * 15 * ... * 35 + 5 * 10 * ... * 35 * 40 
= 5 * 10 * ... * 35 (1 + 40) = 5 * 10 * ... * 35 * 41

Biggest Prime number which will divide above expression is 41

So,  Answer will be E 
Hope it helps!

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If {x} is the product of all integer multiples of 5 from 1 to x, inclu

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If {x} is the product of all integer multiples of 5 from 1 to x, inclu

Prep Toolkit

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