GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 14:47

### 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

# If s is the sum of odd integers from 40 to 60, inclusive, and t is the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Oct 2017
Posts: 20
If s is the sum of odd integers from 40 to 60, inclusive, and t is the  [#permalink]

### Show Tags

12 Oct 2017, 12:33
1
3
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:33) correct 24% (01:53) wrong based on 125 sessions

### HideShow timer Statistics

If s is the sum of odd integers from 40 to 60, inclusive, and t is the number of odd integers from 40 to 60, inclusive, what is s-t?

A. 480
B. 490
C. 980
D. 990
E. 995

Source: Ready4GMAT mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 58340
Re: If s is the sum of odd integers from 40 to 60, inclusive, and t is the  [#permalink]

### Show Tags

12 Oct 2017, 12:39
ladyrenee95 wrote:
If s is the sum of odd integers from 40 to 60, inclusive, and t is the number of odd integers from 40 to 60, inclusive, what is s-t?

A. 480
B. 490
C. 980
D. 990
E. 995

Source: Ready4GMAT mobile app

Similar question: https://gmatclub.com/forum/if-x-is-equa ... 97544.html
_________________
Manager
Joined: 12 Feb 2017
Posts: 70
Re: If s is the sum of odd integers from 40 to 60, inclusive, and t is the  [#permalink]

### Show Tags

12 Oct 2017, 12:48
There are total 10 odd numbers between 40 and 60.
hence, t=10

Now, the given sequence is 41,43,45,......,59
common difference is 2.
hence,
S= (41+59)*(10/2)
S=500.
S-t= 500-10= 490.

Hence, Answer is option B.

Kudos if it helps.
Intern
Joined: 11 Oct 2017
Posts: 20
Re: If s is the sum of odd integers from 40 to 60, inclusive, and t is the  [#permalink]

### Show Tags

12 Oct 2017, 13:31
1
1
Are these formulas correct? I am having trouble with odd numbers for some reason.

N for odd numbers = (Last odd - First odd)/2)) +1

Sum of odd numbers = (First odd + Last odd)*N))/2

1. N = (59-41)/2))+1 = 10

2. Sum of odds = (41+59)*10))/2 = 500

3. 500 - 10 = 490 B

Also, on part 1 of my calculations, do you add one because it is inclusive and do not add one if it is not inclusive?
Senior SC Moderator
Joined: 22 May 2016
Posts: 3545
If s is the sum of odd integers from 40 to 60, inclusive, and t is the  [#permalink]

### Show Tags

12 Oct 2017, 13:36
1
ladyrenee95 wrote:
If s is the sum of odd integers from 40 to 60, inclusive, and t is the number of odd integers from 40 to 60, inclusive, what is s-t?

A. 480
B. 490
C. 980
D. 990
E. 995

Source: Ready4GMAT mobile app

The way I solve sums of arithmetic series, I need the number of terms no matter what. Start there.

Set t

Number of terms: number of odd integers from 40 to 60. First term is 41, last is 59.

Number of terms

$$\frac{LastTerm-FirstTerm}{interval} + 1$$

The "interval" for consecutive even and odds is always 2

$$\frac{59-41}{2} = \frac{18}{2} = (9 + 1)=$$ 10

Set s

Sum of arithmetic series
(Average)(Number of terms) =

$$\frac{FirstTerm+LastTerm}{2}*(10)$$ =

$$\frac{100}{2}(10) = (50)(10) = 500$$

s - t: 500 - 10 = 490

Answer B
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Senior SC Moderator
Joined: 22 May 2016
Posts: 3545
If s is the sum of odd integers from 40 to 60, inclusive, and t is the  [#permalink]

### Show Tags

12 Oct 2017, 14:20
1
ladyrenee95 wrote:
Are these formulas correct? I am having trouble with odd numbers for some reason.

N for odd numbers = (Last odd - First odd)/2)) +1

Sum of odd numbers = (First odd + Last odd)*N))/2

1. N = (59-41)/2))+1 = 10

2. Sum of odds = (41+59)*10))/2 = 500

3. 500 - 10 = 490 B

Also, on part 1 of my calculations, do you add one because it is inclusive and do not add one if it is not inclusive?

ladyrenee95 , sorry, I posted before I saw your questions.

Yes, your method is correct.

I think the reason you might be having trouble with odd numbers is that for consecutive odd integers, the interval (between the numbers), is two. Two is even; that could confuse. Or you might be forgetting to start with the first ODD term (e.g. here, first term is 41, not 40).

Bottom line: The "interval" between 1 and 3 is two. The interval between 2 and 4 is two. For consecutive odds and evens, in the formula, you divide by 2.

Take smaller numbers. Say, sum of odd integers from 0 to 6. So 1 + 3 + 5 = 9. There are three terms (1, 5, 9) whose sum is 9.

Number of terms in "odd integers from 0 to 6":

$$\frac{(Last - First)}{2}+ 1$$

$$\frac{(5-1)}{2} + 1 = (\frac{4}{2}+ 1) = (2 + 1) = 3$$ Correct

SUM: (Average)(# of terms)

$$\frac{(First + Last)}{2}(3)$$

$$\frac{(1 + 5)}{2} (3) = (3)(3) = 9$$
Bingo. Dividing by 2 for consecutive odd integers works.

When subtracting, you add one because subtraction doesn't include the first number. If in doubt: use small numbers that replicate your situation.

For example, # of terms from 1 to 4? The numerals are 1, 2, 3, 4. There are 4 terms. BUT (4 - 1) = 3.
We need one more. 3 + 1 = 4.

There's a mnemonic: "add one before you're done." It almost always applies. If in doubt, replicate your situation with small numbers. Rare in sequence sums but possible: If you see the word "exclusive" or the phrase "exclusive of," that is when you really need to check.

I have seen your other answers using this method. The ones I've seen are correct! (The one about -190 to 195? Correct, but long. -190 to +190 = 0; you are left with only 5 numbers to sum. STILL - correct.)

Here is a fantastically written, comprehensive post on all kinds of sequences by benjiboo , scroll down for arithmetic sequence

And here is a thread on sequences. VeritasPrepKarishma 's posts are great

Hope this barrage of information helps.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Intern
Joined: 11 Apr 2017
Posts: 38
Schools: Kelley '20
Re: If s is the sum of odd integers from 40 to 60, inclusive, and t is the  [#permalink]

### Show Tags

13 Oct 2017, 11:23
N for odd numbers = (Last odd - First odd)/2)) +1

Sum of odd numbers = (First odd + Last odd)*N))/2

1. N = (59-41)/2))+1 = 10

2. Sum of odds = (41+59)*10))/2 = 500

3. 500 - 10 = 490 B
Manager
Joined: 15 Aug 2017
Posts: 76
Location: India
Schools: HBS '22
Re: If s is the sum of odd integers from 40 to 60, inclusive, and t is the  [#permalink]

### Show Tags

01 Aug 2019, 02:20
ladyrenee95 wrote:
If s is the sum of odd integers from 40 to 60, inclusive, and t is the number of odd integers from 40 to 60, inclusive, what is s-t?

A. 480
B. 490
C. 980
D. 990
E. 995

Source: Ready4GMAT mobile app

ScottTargetTestPrep can you please solve this one by the average method. I tried but wasn't able to. The one you used here https://gmatclub.com/forum/what-is-the- ... l#p2153761 Thankyou
_________________
"You don't want to to look back and know you could've done better".
Re: If s is the sum of odd integers from 40 to 60, inclusive, and t is the   [#permalink] 01 Aug 2019, 02:20
Display posts from previous: Sort by

# If s is the sum of odd integers from 40 to 60, inclusive, and t is the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne