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The sum of all the multiples of 3 between 250 and 350
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30 Jul 2018, 10:30
30 Jul 2018, 10:30
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Question Stats:
67% (01:29) correct
32% (02:07) wrong based on 143 sessions
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Quantity A |
Quantity B |
The sum of all the multiples of 3 between 250 and 350 |
9990 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: The sum of all the multiples of 3 between 250 and 350
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07 Aug 2018, 20:28
07 Aug 2018, 20:28
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The first number divisible by \(3\) after \(250\) is \(252\)
The first number divisible by \(3\) before \(350\) is \(348\)
Hence there are altogether \(\frac{348 - 252}{3} + 1 = 33\) numbers
Since the 33 numbers are equally spread apart with a difference of 3 the avg of those numbers = \(\frac{252 + 348}{2} = 300\)
Hence the sum is \(300 * 33 = 9900\)
option B > option A
The first number divisible by \(3\) before \(350\) is \(348\)
Hence there are altogether \(\frac{348 - 252}{3} + 1 = 33\) numbers
Since the 33 numbers are equally spread apart with a difference of 3 the avg of those numbers = \(\frac{252 + 348}{2} = 300\)
Hence the sum is \(300 * 33 = 9900\)
option B > option A
General Discussion
Re: The sum of all the multiples of 3 between 250 and 350
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12 Aug 2018, 06:00
12 Aug 2018, 06:00
4
Expert Reply
Explanation
First, find the smallest multiple of 3 in this range: 250 is not a multiple of 3 (2 + 5 + 0 = 7, which is not a multiple of 3). The smallest multiple of 3 in this range is 252 (2 + 5 + 2 = 9, which is a multiple of 3).
Next, find the largest multiple of 3 in this range. Since 350 is not a multiple of 3 (3 + 5 + 0 = 8), the largest multiple of 3 in this range is 348.
The sum of an evenly spaced set of numbers equals the average value multiplied by the number of terms. The average value is the midpoint between 252 and 348: (252 + 348) ÷ 2 = 300. To find the number of terms, first subtract 348 – 252 = 96. This figure represents all numbers between 348 and 252, inclusive.
To count only the multiples of 3, divide 96 by the 3: 96 ÷ 3 = 32. Finally, “add 1 before you’re done” to count both end points of the range: 32 + 1 = 33.
The sum is 300 × 33 = 9,900. Since 9,900 is smaller than 9,990, Quantity B is greater.
First, find the smallest multiple of 3 in this range: 250 is not a multiple of 3 (2 + 5 + 0 = 7, which is not a multiple of 3). The smallest multiple of 3 in this range is 252 (2 + 5 + 2 = 9, which is a multiple of 3).
Next, find the largest multiple of 3 in this range. Since 350 is not a multiple of 3 (3 + 5 + 0 = 8), the largest multiple of 3 in this range is 348.
The sum of an evenly spaced set of numbers equals the average value multiplied by the number of terms. The average value is the midpoint between 252 and 348: (252 + 348) ÷ 2 = 300. To find the number of terms, first subtract 348 – 252 = 96. This figure represents all numbers between 348 and 252, inclusive.
To count only the multiples of 3, divide 96 by the 3: 96 ÷ 3 = 32. Finally, “add 1 before you’re done” to count both end points of the range: 32 + 1 = 33.
The sum is 300 × 33 = 9,900. Since 9,900 is smaller than 9,990, Quantity B is greater.
