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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 [#permalink]

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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
[Reveal] Spoiler: OA

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Re: If {x} is the product of all integer multiples of 5 from 1 to x, inclu [#permalink]

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New post 02 Oct 2017, 00:38
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Bunuel wrote:
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


{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
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Re: If {x} is the product of all integer multiples of 5 from 1 to x, inclu [#permalink]

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New post 03 Oct 2017, 08:34
{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

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Re: If {x} is the product of all integer multiples of 5 from 1 to x, inclu [#permalink]

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New post 04 Oct 2017, 15:37
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Bunuel wrote:
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


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
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Re: If {x} is the product of all integer multiples of 5 from 1 to x, inclu [#permalink]

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New post 07 Oct 2017, 02:16
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!

Kudos [?]: 0 [0], given: 0

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Re: If {x} is the product of all integer multiples of 5 from 1 to x, inclu [#permalink]

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New post 07 Oct 2017, 02:24
Expert's post
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lor12345 wrote:
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



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!


{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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135818 [0], given: 12715

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Joined: 26 Sep 2017
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Re: If {x} is the product of all integer multiples of 5 from 1 to x, inclu [#permalink]

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New post 08 Oct 2017, 08:05
Bunuel wrote:
lor12345 wrote:
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



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!


{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.

Thank you! Yes, now it's clear!

Kudos [?]: 0 [0], given: 0

Re: If {x} is the product of all integer multiples of 5 from 1 to x, inclu   [#permalink] 08 Oct 2017, 08:05
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