Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Jun 2015
Posts: 184
Location: Ghana

If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
07 Sep 2016, 10:25
Question Stats:
56% (01:32) correct 44% (01:34) wrong based on 220 sessions
HideShow timer Statistics
If x = a!, which of the following values of a is the least possible value for which the last 8 digits of the integer x will all be zero? A) 21 B) 29 C) 38 D) 40 E) 100
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Kindly press kudos if you find my post helpful



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3580

If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
07 Sep 2016, 10:44
duahsolo wrote: If x = a!, which of the following values of a is the least possible value for which the last 8 digits of the integer x will all be zero? A) 21 B) 29 C) 38 D) 40 E) 100 We need to find out the No. of 5s in a! to find out the number of zeros at the end. Option A = 21/5 = 4. Hence, max 5s are 4. Hence, max zero would be 4. Option B = 29/5 = 5/5 = 1. Hence, max 5s are 6 Hence, max zero would be 6. Option C = 38/5 = 7/5 = 1. Hence, max 5s are 8 Hence, max zero would be 8. Hence, the answer C
_________________
My LinkedIn abhimahna.My GMAT Story: From V21 to V40My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeBlog: Subscribe to Question of the Day BlogGMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here. New! Best Reply Functionality on GMAT Club!Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.



Manager
Joined: 26 Mar 2016
Posts: 69
Location: Greece
GPA: 2.9

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
25 Sep 2016, 05:59
(A) 21/5 + 21/5^2= 4+0=4 5s, therefore 4 0s. (B) 29/5 + 29/5^2= 5+1=6 5s, therefore 6 0s. (C) 38/5 + 38/5^2= 7+1=8 5s, so 8 0s. Correct
_________________
+1 Kudos if you like the post



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
25 Sep 2016, 06:15
duahsolo wrote: If x = a!, which of the following values of a is the least possible value for which the last 8 digits of the integer x will all be zero? A) 21 B) 29 C) 38 D) 40 E) 100 a! must have 8 trailing zeroes... We know that in order to have 8 trailing zero's we must decide a by 5 and continue the process till be get answer 8 or More than 8 a/5 = 8 So, a ~ 40 Or, a must be close to 40... Check options close to 40 , Only option (C) and (D) in this case... Check option (C) 38/5 = 7 7/5 = 1 So, Option (C) is correct... PS: I just used approximation to arrive at the answer quickly
_________________



Intern
Joined: 05 Feb 2016
Posts: 1

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
25 Sep 2016, 08:52
Why should we find the No. of 5s in a!. I don't understand. And what do you mean by 5s? For example, number 21 has 5,10,15,20  so, 4 times 5s. Is this what you mean by the number of 5s?



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3580

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
25 Sep 2016, 09:00
Krasniqi123 wrote: Why should we find the No. of 5s in a!. I don't understand. And what do you mean by 5s? For example, number 21 has 5,10,15,20  so, 4 times 5s. Is this what you mean by the number of 5s? One zero will come when we multiply a number with 10. Now, 10 = 2 *5 Out of the 2 and 5, we will always have the number of 5s less than the number of 2's. Hence, if we find the number of 5's we will atleast have that many 2's but the vice viersa is not true. hence, we are find the number of 5's Think it like this : in 10!, we will have more 2's than 5's. So, I can say 10/5 = 2 5's are present in 10! if we find the number of 2's, I will get 10/2 = 5 / 2= 2 or 5+2 = 7 2's. But since we have only 2 5's we have only two zero's at the end of 10!. I hope the concept is clear now.
_________________
My LinkedIn abhimahna.My GMAT Story: From V21 to V40My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeBlog: Subscribe to Question of the Day BlogGMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here. New! Best Reply Functionality on GMAT Club!Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
25 Sep 2016, 09:04
Krasniqi123 wrote: Why should we find the No. of 5s in a!. I don't understand. And what do you mean by 5s? For example, number 21 has 5,10,15,20  so, 4 times 5s. Is this what you mean by the number of 5s? Go through the concept on Factorials in our GMAT Quantz Book Here  mathnumbertheory88376.html#p666609Hope this will surely help you..
_________________



Board of Directors
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
24 Oct 2016, 06:59
duahsolo wrote: If x = a!, which of the following values of a is the least possible value for which the last 8 digits of the integer x will all be zero? A) 21 B) 29 C) 38 D) 40 E) 100 i think this question is testing our knowledge of trailing zeroes... to have 8 digits of zero in the end, we need to have 8 factors of two, and 8 factors of 5. let's see. since we can very fast get to 8 factors of two, let's see how we can get to 8 factors of 5... 5 (1),... 10 (2), ... 15 (3), ... 20 (4), ... 25 (6), ... 30 (7), ... 35 (8). A, B are right away out. since we need the least possible value, 38 works... C is the answer.



Senior Manager
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
12 Dec 2016, 05:24
duahsolo wrote: If x = a!, which of the following values of a is the least possible value for which the last 8 digits of the integer x will all be zero? A) 21 B) 29 C) 38 D) 40 E) 100 We have infinite series which sum approximately equals to \(8\) \(\frac{a}{5} + \frac{a}{5^2} + \frac{a}{5^3} + … ≈ 8\) \(\frac{a}{5} / (1  \frac{1}{5}) ≈ 8\) \(a ≈ 32\) \([\frac{32}{5}] + [\frac{32}{25}] = 7\) From 30 to 34 to 34 there are 7 trailing zeros. From 35 to 39 there are 8 trailing zeros. Answer C.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
13 Dec 2016, 17:49
duahsolo wrote: If x = a!, which of the following values of a is the least possible value for which the last 8 digits of the integer x will all be zero? A) 21 B) 29 C) 38 D) 40 E) 100 We are given that x = a! and need to determine the least value for a that will create 8 trailing zeros in integer x. We must remember that a trailing zero is created with each 5and2 pair within the prime factorization of a!. Furthermore, since we know there are fewer 5s in a! (or any factorial) than 2s, we can find the number of 5s and thus be able to determine the number of 5and2 pairs. Let’s test answer choice A: To determine the number of 5s within 21!, we can use the following shortcut in which we divide 21 by 5, and then divide the quotient of 21/5 by 5 and continue this process until we no longer get a nonzero quotient: 21/5 = 4 (we can ignore the remainder) Since 4/5 does not produce a nonzero quotient, we can stop. 21! contains four 5and2 pairs, and thus 21! does not contain 8 trailing zeros. Next we can test answer choice B: 29/5 = 5 (we can ignore the remainder) 5/5 =1 (we can ignore the remainder) Since 1/5 does not produce a nonzero quotient, we can stop. The final step is to add up our quotients; that sum represents the number of factors of 5 within 29!. Thus, there are 5 + 1 = 6 factors of 5 within 29! 29! contains six 5and2 pairs, and thus 29! does not contain 8 trailing zeros. Next we can test answer choice C: 38/5 = 7 (we can ignore the remainder) 7/5 =1 (we can ignore the remainder) Since 1/5 does not produce a nonzero quotient, we can stop. The final step is to add up our quotients; that sum represents the number of factors of 5 within 38!. Thus, there are 7 + 1 = 8 factors of 5 within 38! 38! contains eight 5and2 pairs, and thus 38! does contain 8 trailing zeros. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Current Student
Joined: 20 Jan 2017
Posts: 51
Location: United States (NY)
GMAT 1: 750 Q48 V44 GMAT 2: 610 Q34 V41
GPA: 3.92

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
24 Jan 2017, 19:40
1) We need to find the first 8 5's in the sequence of consecutive integers: 5*10*15*20*25(5*5)*30*35 2) 35 is the smallest value of a, but from the given choices, it is 38
The correct answer is C



Director
Joined: 24 Nov 2016
Posts: 618
Location: United States

Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
Show Tags
12 Aug 2019, 05:56
duahsolo wrote: If x = a!, which of the following values of a is the least possible value for which the last 8 digits of the integer x will all be zero? A) 21 B) 29 C) 38 D) 40 E) 100 num of zeros in a factorial \(n!\) is the sum of the quotients of \(n\) divided by \(5^1,5^2,5^3,5^4…\) num of zeros in \(40!\) is \(40/5+40/25=8+1=9\) least possible value for which the last 8 digits are zeros must be a \(35≤factorial<40\) Answer (C).




Re: If x = a!, which of the following values of a is the least possible va
[#permalink]
12 Aug 2019, 05:56






