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The sum of all the integers
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23 Feb 2021, 02:11
23 Feb 2021, 02:11
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Question Stats:
86% (00:27) correct
13% (00:43) wrong based on 29 sessions
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Quantity A |
Quantity B |
The sum of all the integers from 1 to 20 |
210 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
The sum of all the integers
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23 Feb 2021, 04:32
23 Feb 2021, 04:32
1
Hi,
You can do this question by two methods.
Approach 1:
Sum of all integers= \(\frac{n(n+1)}{2}\)
=\(\frac{20(21)}{2}\)
=210
QTY A= QTY B
Approach 2:
Consider the first and last digits of the set: 20 &1 the sum is 21.
Consider the second and second last digit of the set 19+2=21
Similarly all the digits 18&3, 17&4 etc will have a total of 21 and there will be 10 such sets.
This, 21x10=210
QTY A= QTY B
IMO C
Hope this helps!
Posted from my mobile device
You can do this question by two methods.
Approach 1:
Sum of all integers= \(\frac{n(n+1)}{2}\)
=\(\frac{20(21)}{2}\)
=210
QTY A= QTY B
Approach 2:
Consider the first and last digits of the set: 20 &1 the sum is 21.
Consider the second and second last digit of the set 19+2=21
Similarly all the digits 18&3, 17&4 etc will have a total of 21 and there will be 10 such sets.
This, 21x10=210
QTY A= QTY B
IMO C
Hope this helps!
Posted from my mobile device
Re: The sum of all the integers
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23 Feb 2021, 07:50
23 Feb 2021, 07:50
2
Another approach for answer is:
Find the mid value which is \(\frac{(20+1)}{2}\) = 10.5
Find the total number of terms \((20-1)+1\) = 20; Since both 20 and 1 needs to be counted for finding the total terms.
Hence, answer is \(10.5 * 20\) = 210.
Find the mid value which is \(\frac{(20+1)}{2}\) = 10.5
Find the total number of terms \((20-1)+1\) = 20; Since both 20 and 1 needs to be counted for finding the total terms.
Hence, answer is \(10.5 * 20\) = 210.
