Last visit was: 19 Jul 2025, 14:10 It is currently 19 Jul 2025, 14:10
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
gmihir
Joined: 04 Mar 2012
Last visit: 06 Jun 2012
Posts: 34
Own Kudos:
1,597
 [125]
Given Kudos: 10
Posts: 34
Kudos: 1,597
 [125]
7
Kudos
Add Kudos
118
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
mbaiseasy
Joined: 13 Aug 2012
Last visit: 29 Dec 2013
Posts: 323
Own Kudos:
1,993
 [71]
Given Kudos: 11
Concentration: Marketing, Finance
GPA: 3.23
Posts: 323
Kudos: 1,993
 [71]
43
Kudos
Add Kudos
27
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 July 2025
Posts: 102,625
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,625
Kudos: 742,778
 [67]
30
Kudos
Add Kudos
36
Bookmarks
Bookmark this Post
General Discussion
avatar
Ousmane
Joined: 11 Jul 2012
Last visit: 28 Sep 2018
Posts: 35
Own Kudos:
Posts: 35
Kudos: 26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I got 0.2 too (B). Please help. Here is my approach
(1/45) + (1/46) + .....+(1/54) = (45-44)/45 +(46-45)/46 +.....+(54-53)/54
= 10 -(44/45 + 45/46 + ...53/54). Each term in the bracket is > 0.977, and there are ten of them. Then their sum is roughly 9.8
10-9.8 = 0.2. But is this doable in 2 mn under stress and heat?
Brother Karamazov



Brother Karamazov
avatar
watwazdaquestion
Joined: 18 Jul 2012
Last visit: 14 Dec 2012
Posts: 15
Own Kudos:
21
 [2]
Given Kudos: 1
Status:wants to beat the gmat
Location: United States
Posts: 15
Kudos: 21
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
my method was 1/45 + 1/46 + ... => 10/45 ~ 2/9 ~ .2
User avatar
TeamGMATIFY
Joined: 20 Aug 2015
Last visit: 31 Oct 2016
Posts: 340
Own Kudos:
1,488
 [10]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Expert
Expert reply
GMAT 1: 760 Q50 V44
Posts: 340
Kudos: 1,488
 [10]
10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmihir
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

Such questions do not test your calculations. (In fact most of GMAT questions) They test your logic and how easily can you simplify a problem.
That is why an approximate result is asked and not the absolute value.


Out of the given numbers, from 45 to 54, carrying out calculations with 50 would be easiest.

Hene instead of 1/45 + 1/46 + ... 1/50 + ... + 1/54,
We can increase some terms and decrease some terms by changing the numbers with 50

Hence we have a sequence = 1/50 + 1/50 + ... + 1/50 (Total 20 terms)
= 10/50 = 1/5 = 0.2 approximately
Option B
avatar
BoomHH
Joined: 26 Dec 2016
Last visit: 11 Jun 2017
Posts: 9
Own Kudos:
8
 [1]
Given Kudos: 13
Posts: 9
Kudos: 8
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
TeamGMATIFY
gmihir
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

Such questions do not test your calculations. (In fact most of GMAT questions) They test your logic and how easily can you simplify a problem.
That is why an approximate result is asked and not the absolute value.


Out of the given numbers, from 45 to 54, carrying out calculations with 50 would be easiest.

Hene instead of 1/45 + 1/46 + ... 1/50 + ... + 1/54,
We can increase some terms and decrease some terms by changing the numbers with 50

Hence we have a sequence = 1/50 + 1/50 + ... + 1/50 (Total 20 terms)
= 10/50 = 1/5 = 0.2 approximately
Option B

Hi,

aren't there 10 terms and not 20 ?

regards
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,996
Own Kudos:
7,952
 [10]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,996
Kudos: 7,952
 [10]
5
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
gmihir
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

We need to determine the approximate value of the sum of the reciprocals from 45 to 54 inclusive; thus, we need the approximate value of the following:

1/45 + 1/46 + 1/47 + 1/48 + 1/49 + 1/50 + 1/51 + 1/52 + 1/53 + 1/54

Rather than adding each of these numbers (which would be incredibly time-consuming), let’s strategically select one of the fractions in our list and add it to itself 10 times. That sum will give us an approximate value for S.

Scanning the list, we see the best number to add to itself 10 times is 1/50. However, instead of actually adding 1/50 ten times, we will simply multiply it by 10:

1/50 x 10 = 10/50 = 1/5 = 0.2

Thus, we see that S is approximately 0.2.

Answer: B
User avatar
gracie
Joined: 07 Dec 2014
Last visit: 11 Oct 2020
Posts: 1,035
Own Kudos:
1,862
 [2]
Given Kudos: 27
Posts: 1,035
Kudos: 1,862
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
gmihir
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

median=49.5
reciprocal=2/99
10*(2/99)=20/99≈.2
B
avatar
Siverma
Joined: 22 Sep 2018
Last visit: 30 Jun 2019
Posts: 1
Own Kudos:
Given Kudos: 8
Location: Canada
Concentration: Finance, General Management
GPA: 2.85
WE:Other (Insurance)
Posts: 1
Kudos: 5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Mid point of the range 45-54 is 50. So if we take the reciprocal of 50 and add it 10 times as per the question, we get 1/5 which is 0.2

We take 50 as the average of the range and do the simplified math.
User avatar
dabaobao
Joined: 24 Oct 2016
Last visit: 20 Jun 2022
Posts: 572
Own Kudos:
Given Kudos: 143
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
GMAT 3: 690 Q48 V37
GMAT 4: 710 Q49 V38 (Online)
GMAT 4: 710 Q49 V38 (Online)
Posts: 572
Kudos: 1,557
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmihir
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5


# of Terms = (54-45)/1 + 1 = 10

Method 1: Using First & Last Term
Mean = ((1/45) + (1/54))/2 = (54+45)/(45*54*2) = 99/(45*54*2)
= 33/(15*54*2) = 11/(5*54*2) = 11/540
Sum = 10 * 11/540 = 110/540 = 0.2 => B

Method 2: Using Middle Terms (Better)
Mean Number = (1/49 + 1/50)/2 = ~1/50
Sum = 10/50 = 0.2 => B
avatar
hasanloubani
Joined: 27 Jan 2020
Last visit: 12 Jan 2021
Posts: 12
Own Kudos:
Given Kudos: 1,029
Posts: 12
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mbaiseasy
gmihir
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

Sorry, don't have an official answer.

Solved this using Bunuel's technique that I saw on another similar problem.

S = \(\frac{1}{45}+\frac{1}{46}+...+\frac{1}{54}\)

Get number of terms: \(54 - 45 + 1 = 10\)

Get lower limit: \(10*\frac{1}{54}=\frac{5}{27}=0.18\)
Get upper limit: \(10*\frac{1}{45}=\frac{2}{9}=0.22\)

\(0.18<S<0.22\)

how do you calculate decimals of high denominator value plz?

Answer: B
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 19 Jul 2025
Posts: 4,145
Own Kudos:
Given Kudos: 98
 Q51  V47
Expert
Expert reply
Posts: 4,145
Kudos: 10,640
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hasanloubani
how do you calculate decimals of high denominator value plz?

That's not something you need to do here - if you notice we're adding ten fractions roughly equal to 1/50, the sum will roughly be 10/50. Or you can notice we're adding ten things that are all less than or equal to 1/45, and also are adding ten things greater than or equal to 1/54. So

10/54 < S < 10/45

and 10/50 = 0.2 is the only value from among the answer choices that S can approximately equal.

If you did want to find the decimal equivalents of 10/45 and 10/54, in the first case, 10/45 = 2/9. You can find the decimal of 2/9 if you know the decimal of 1/3:

1/3 = 0.33333....

so dividing by 3 on both sides

1/9 = 0.1111....

and multiplying by 2 on both sides

2/9 = 0.2222....

We can do something similar for 10/54, though it's a bit trickier. Since 10/54 = 5/27, we can start from

1/9 = 0.111111....

and divide by 3 on both sides (using the fact that 111/3 = 37) to get

1/27 = 0.037037....

and then multiply by 5 to get

5/27 = 0.185185....

So for these specific fractions, you can find their decimal equivalent without using long division, because their denominators are somewhat convenient to work with. But in general, if you invent a fraction with a random denominator, most of the time you'd have no practical choice other than long division to find the decimal. So if you need the decimal equivalent of 3/29, say, you'd need to use long division (or a calculator) to find it. Fortunately you never need to do that on the GMAT -- all you might need to notice on the GMAT is that 3/29 is very slightly larger than 3/30, so is very slightly larger than 0.1.
User avatar
Fdambro294
Joined: 10 Jul 2019
Last visit: 06 Apr 2025
Posts: 1,353
Own Kudos:
Given Kudos: 1,658
Posts: 1,353
Kudos: 707
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmihir
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5

We have the sum of 10 numbers:

(1/45) + (1/46) + …… + (1/54) =

(1st)
The sum must be less to the value if we were to assume that all 10 numbers were equal to the highest value: 1/45

1/45 = (1/9) * (1/5) = (1/9) * (.2) = .2 / 9

= .0222222…..

And

(10) (.02222….) = .222222…

sum < .222222…..

only A and B are possible


(2nd)
The sum must be greater than > (10) (1/54)

(10 / 54) = (5/27) = (5/9) * (1/3) = (.555..) * (1/3)

When we divide 3 into the recurring decimal (.555…) we get approximately .185


(.185) < sum < (.2222…)

*B* is the only possible answer

Posted from my mobile device
User avatar
jsam98
Joined: 07 May 2024
Last visit: 09 Jun 2025
Posts: 14
Own Kudos:
Given Kudos: 20
Posts: 14
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
watwazdaquestion
my method was 1/45 + 1/46 + ... => 10/45 ~ 2/9 ~ .2
This should make u more worried to check 0.2 as answer coz 10 * 1/45 will give u the maximum possible sum of that sequence starting from 1/45 the answer should be less then 0.2 [0.1 will be v appealing if u are in hurry]
Moderators:
Math Expert
102625 posts
PS Forum Moderator
698 posts