Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46291

Question Stats:
47% (00:40) correct 53% (00:35) wrong based on 57 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 46291

Re M3201 [#permalink]
Show Tags
21 May 2016, 04:21
Official Solution:How many trailing zeroes does \(49! + 50!\) have?A. 9 B. 10 C. 11 D. 12 E. 22 Factor out 49! from the expression: \(49! + 50!=49!(1+50)=49!*51\). 51 won't contribute to the number of zeros at the end of the number, therefore all zeros will come from 49!. Trailing zeros in 49!: \(\frac{49}{5}+\frac{49}{5^2}=9+1=10\) THEORY: Trailing zeros: Trailing zeros are a sequence of 0's in the decimal representation of a number, after which no other digits follow. For example 125,000 has 3 trailing zeros; The number of trailing zeros n!, the factorial of a nonnegative integer \(n\), can be determined with this formula: \(\frac{n}{5}+\frac{n}{5^2}+\frac{n}{5^3}+...+\frac{n}{5^k}\), where \(k\) must be chosen such that \(5^{(k+1)} \gt n\) It's easier if we consider an example: How many zeros are in the end (after which no other digits follow) of 32!? \(\frac{32}{5}+\frac{32}{5^2}=6+1=7\). Notice that the last denominator (\(5^2\)) must be less than 32. Also notice that we take into account only the quotient of the division, that is \(\frac{32}{5}=6\). So there are 7 zeros in the end of 32!. Another example, how many trailing zeros does 125! have? \(\frac{125}{5}+\frac{125}{5^2}+\frac{125}{5^3}=25+5+1=31\), The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero. Answer: B
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 12 Nov 2015
Posts: 60
Location: Uruguay
Concentration: General Management
GMAT 1: 610 Q41 V32 GMAT 2: 620 Q45 V31 GMAT 3: 640 Q46 V32
GPA: 3.97

Re: M3201 [#permalink]
Show Tags
28 May 2016, 10:10
Hello, Please help me out in understanding why the answer is 10 and not 11. 49! has 10 trailing zeros OK. But 49!(10*5+1)? doesn't the 10 in the expression add an extra zero to the trailing zeros of 49! ?



Math Expert
Joined: 02 Aug 2009
Posts: 5933

Re: M3201 [#permalink]
Show Tags
28 May 2016, 10:19
Avigano wrote: Hello, Please help me out in understanding why the answer is 10 and not 11. 49! has 10 trailing zeros OK. But 49!(10*5+1)? doesn't the 10 in the expression add an extra zero to the trailing zeros of 49! ? Hi, no, 49!(10*5+1) = 49!(50+1) = 49!*51... Now 51 does not contain any 5 in it, so the term depends on ONLY 49! and as you have said 49! has 10 5s so ans is 10
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Current Student
Joined: 12 Nov 2015
Posts: 60
Location: Uruguay
Concentration: General Management
GMAT 1: 610 Q41 V32 GMAT 2: 620 Q45 V31 GMAT 3: 640 Q46 V32
GPA: 3.97

Re: M3201 [#permalink]
Show Tags
28 May 2016, 10:38
chetan2u wrote: Avigano wrote: Hello, Please help me out in understanding why the answer is 10 and not 11. 49! has 10 trailing zeros OK. But 49!(10*5+1)? doesn't the 10 in the expression add an extra zero to the trailing zeros of 49! ? Hi, no, 49!(10*5+1) = 49!(50+1) = 49!*51... Now 51 does not contain any 5 in it, so the term depends on ONLY 49! and as you have said 49! has 10 5s so ans is 10 Ok! got it! thanks



Manager
Joined: 13 Dec 2013
Posts: 162
Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: M3201 [#permalink]
Show Tags
29 Dec 2016, 14:13
chetan2u wrote: Avigano wrote: Hello, Please help me out in understanding why the answer is 10 and not 11. 49! has 10 trailing zeros OK. But 49!(10*5+1)? doesn't the 10 in the expression add an extra zero to the trailing zeros of 49! ? Hi, no, 49!(10*5+1) = 49!(50+1) = 49!*51... Now 51 does not contain any 5 in it, so the term depends on ONLY 49! and as you have said 49! has 10 5s so ans is 10 Hi All  I don't 100% understand the rationale behind 51 not contributing to the number of trailing zeros. Does 51 not contain 10^1? Thanks.



Intern
Joined: 21 May 2016
Posts: 8

Re: M3201 [#permalink]
Show Tags
29 Dec 2016, 22:28
Dear Bunuel,
I know the concept and deduced the final step 49! * 51. But 49/5 = 9.8 ~ 10 and 49/25 =1.96 ~ 2 .So I marked the answer as 12 instead of 10.Please clarify,if we need to select the lowest rounded integer or do we need to consider the nearest rounded integer to answer these kind of questions.



Math Expert
Joined: 02 Sep 2009
Posts: 46291

Re: M3201 [#permalink]
Show Tags
30 Dec 2016, 00:37



Manager
Joined: 13 Dec 2013
Posts: 162
Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: M3201 [#permalink]
Show Tags
04 Jan 2017, 14:55
chetan2u wrote: Avigano wrote: Hello, Please help me out in understanding why the answer is 10 and not 11. 49! has 10 trailing zeros OK. But 49!(10*5+1)? doesn't the 10 in the expression add an extra zero to the trailing zeros of 49! ? Hi, no, 49!(10*5+1) = 49!(50+1) = 49!*51... Now 51 does not contain any 5 in it, so the term depends on ONLY 49! and as you have said 49! has 10 5s so ans is 10 Hi. How does 51 not contain any 5s?



Math Expert
Joined: 02 Sep 2009
Posts: 46291

Re: M3201 [#permalink]
Show Tags
05 Jan 2017, 03:23



Intern
Joined: 12 May 2016
Posts: 7
Location: India
GPA: 3.93

Re M3201 [#permalink]
Show Tags
20 Jan 2017, 10:16
I think this is a highquality question.



Intern
Joined: 16 Nov 2016
Posts: 30
Location: India
Concentration: Finance, International Business
GPA: 3.78
WE: Accounting (Accounting)

Re: M3201 [#permalink]
Show Tags
17 Mar 2017, 22:05
Sorry i have a question. what is wrong if you factor 49 and 50 factorial and add?? So you will get 22



Math Expert
Joined: 02 Sep 2009
Posts: 46291

Re: M3201 [#permalink]
Show Tags
18 Mar 2017, 02:09



Manager
Joined: 19 Aug 2016
Posts: 153
Location: India
GPA: 3.82

Re: M3201 [#permalink]
Show Tags
15 Jul 2017, 13:08
Hi, I solved with the trailing zero method only but I calculated for 49! and 50! separately and I got 22 as answer. I want to know how that is a wrong method of solving. Thanks!
_________________
Consider giving me Kudos if you find my posts useful, challenging and helpful!



Math Expert
Joined: 02 Sep 2009
Posts: 46291

Re: M3201 [#permalink]
Show Tags
16 Jul 2017, 04:14



Intern
Joined: 04 Dec 2014
Posts: 1

Re: M3201 [#permalink]
Show Tags
30 Sep 2017, 10:04
This was confusing for me too, but the logic lies in the fact that 49! is a factorial. 1x2x3x4....40x41x...49. vs. 51 which is just 17x3. There are no 5s in 51. The formula allows you to count how many 5s are in factorials. If it was 51! (factorial) then yes it would have 12 fives, but the answer is 10 because 51 is NOT a factorial in this problem (after you simplify it.)



Intern
Joined: 16 Oct 2017
Posts: 5
Location: India
GPA: 3.67

Re M3201 [#permalink]
Show Tags
04 May 2018, 22:48
I think this is a highquality question and I agree with explanation. This about the 51 that is left out. When we multiply 51 with 10^n. The answer always is giving (n1) trailing zeros. Example, 10*51=51 (1vs0),100*51=510 (2vs1), 1000*51=5100 (3vs2). So i got 10 Trailing zeros for 49! but since it is being multiplied by 51 I assumed it would remove 1 zero from the total and give 9 trailing zeros. Please let me know where i have done a mistake.



Math Expert
Joined: 02 Sep 2009
Posts: 46291

Re: M3201 [#permalink]
Show Tags
05 May 2018, 00:16
kittyman wrote: I think this is a highquality question and I agree with explanation. This about the 51 that is left out. When we multiply 51 with 10^n. The answer always is giving (n1) trailing zeros. Example, 10*51=51 (1vs0),100*51=510 (2vs1), 1000*51=5100 (3vs2). So i got 10 Trailing zeros for 49! but since it is being multiplied by 51 I assumed it would remove 1 zero from the total and give 9 trailing zeros. Please let me know where i have done a mistake. Not sure what are you doing there. 10*51 = 510 not 51. 100*51 = 5,100 no 510. 1,000*51 = 51,000 no 5,100. 10^n, where n is a positive integer, will have n trailing zeros.
_________________
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? Extrahard Quant Tests with Brilliant Analytics










