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How many multiples of 7 are there between 700 and 1000, inclusive?

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How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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New post 26 Sep 2016, 03:01
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How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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New post 26 Sep 2016, 05:38
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20



This is how I tried...

There are exactly 301 numbers between 700 to 1000..

701 to 800 = 100
801 to 1000 = 200...Total 300 numbers , count 700 too..

301/7 = 43...

IMO option A.
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Re: How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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New post 26 Sep 2016, 06:05
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Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20



`Smallest 7 digit number divisible by 7 = 700 here
Largest div by 7 = 994

994-700 = 294
Now, 294/7 = 42
Add 1

Answer = 43
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How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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New post 26 Sep 2016, 10:24
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anki2762 wrote:
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20



`Smallest 7 digit number divisible by 7 = 700 here
Largest div by 7 = 994

994-700 = 294
Now, 294/7 = 42
Add 1

Answer = 43


Arithmetic Progression Approach !!!

Please correct the Highlighted part in RED ... I am sure U meant Number divisible by 7 and Not 7 Digit Number...

Now, in the AP series - { 700, 707, 714............994 }

\(a\) = 700 ( Smallest Number )
\(d\) = 7 ( common Difference )
\(l\) = 994 ( Largest Number )

No of Terms = \(\frac{( l - a )}{d} + 1\)

No of Terms = \(\frac{( 994 - 700 )}{d} + 1\)

No of Terms = \(42+ 1\)

No of Terms = \(43\)

Hence answer will be (A) 43

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Re: How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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New post 21 Jul 2018, 02:45
msk0657 wrote:
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20



This is how I tried...

There are exactly 301 numbers between 700 to 1000..

701 to 800 = 100
801 to 1000 = 200...Total 300 numbers , count 700 too..

301/7 = 43...

IMO option A.


Even though your approach seems bizarre, you have got the right answer. One should find the least and the largest number that is divisible by 7. The least number between 700-1000 that is the multiple of 7 is 700 and the largest is 994. We subtract 700 from 994 to get the numbers of the range, which is 294. Meanwhile, the inclusion means that we should also take into account 994 itself. When we count the possibilities through 294, we ignore 994 itself.
In the range of 1-10, when you subtract 10-1=9 which itself omits 10 from the range. The same applies to the problem.
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Re: How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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New post 07 Sep 2018, 17:13
Two ways of solving the above question

either \(1,000 - 700 = 300 + 1 = \frac{301}{7} = 43\)
or \(100*7 = 700\) and \(142 * 7 = 994\) then \(142 - 100 = 42 + 1 = 43\)
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How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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New post 07 Sep 2018, 19:01
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20

To find the number of terms, we can use
\(\frac{LastTerm-FirstTerm}{Increment}+1\)

(Some people use the quip "add one before you're done.")

First Term: \(700\)

Last Term? Divide 1,000 by 7

1)\(\frac{1,000}{7}=42.xx\). That is, (42*7) is the highest we can go
2) So the Last Term is \((42*7)=994\)

Number of terms? Increment = 7: \((\frac{994-700}{7}+1)=(\frac{294}{7}+1)=(42+1)=43\)

ANSWER A

For an excellent post on sequences, including how to find number of terms, see Guide to Sequences and Series, HERE (scroll to Part 2 for Number of Terms)

See also Sequences Made Easy, HERE.

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How many multiples of 7 are there between 700 and 1000, inclusive?   [#permalink] 07 Sep 2018, 19:01
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