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Let x and y be defined as the sum of all integers between x and y.

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Bunuel
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Let x and y be defined as the sum of all integers between x and y. [#permalink] New post   30 Sep 2021, 06:15
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Let \(x \divideontimes y\) be defined as the sum of all integers between 𝑥 and 𝑦. For example, \(1 \divideontimes 4=2+3=5\). What is the value of \((60 \divideontimes 900)-(63 \divideontimes 898)\)?

A. 1980
B. 1981
C. 1982
D. 1983
E. 1984
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D
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Re: Let x and y be defined as the sum of all integers between x and y. [#permalink] New post   30 Sep 2021, 06:38
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(60⋇900) = 61+62+63+64+65…+897+898+899
(63⋇898) = 64+65+…+897
___________________________________________
Thus, (60⋇900)- (63⋇898) = 61+62+63+898+899 = 1983

Answer (D)
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BrentGMATPrepNow
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Let x and y be defined as the sum of all integers between x and y. [#permalink] New post   30 Sep 2021, 07:28
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Bunuel wrote:
Let \(x \divideontimes y\) be defined as the sum of all integers between 𝑥 and 𝑦. For example, \(1 \divideontimes 4=2+3=5\). What is the value of \((60 \divideontimes 900)-(63 \divideontimes 898)\)?

A. 1980
B. 1981
C. 1982
D. 1983
E. 1984


\(60 \divideontimes 900 =\) 61+62+63+64+65+. . . . +897+898+899

\(63 \divideontimes 898 =\) 64+65+66+. . . . 896+897

So, \((60 \divideontimes 900)-(63 \divideontimes 898)\) = (61+62+63+64+65+. . . . +897+898+899) - (64+65+66+. . . . 896+897)
= 61+62+63+898+899

NOTE: Before adding all 5 numbers together, we should first scan the answer choices. Since all 5 options have DIFFERENT units digits, we can simply follow the units digits...

61 + 62 + 63 + 898 + 899 = 61 + 62 + 63 + 898 + 899 = ???3

Answer: D
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Re: Let x and y be defined as the sum of all integers between x and y. [#permalink] New post   19 Apr 2024, 05:53
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧



\((60 \divideontimes 900) - (63 \divideontimes 898)\)
= Sum of all the integers between 60 and 900 - Sum of all the integers between 63 and 898
= (61 + 62 + .... + 896 + 897 + 898 + 899) - ( 64 + 65 + .... + 896 + 897)
= 61 + 62 + 63 + 898 + 899

Now if you look at the answer choices then all the options have different units' digit
=> 1 + 2 + 3 + 8 + 9
=> Units' digit of 3
=> 1983 is the answer

So, Answer will be D
Hope it helps!

Watch the following video to MASTER Functions and Custom Characters

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GMAT Club Bot
gmatclubot
Re: Let x and y be defined as the sum of all integers between x and y. [#permalink]
19 Apr 2024, 05:53
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