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huongguyen
Joined: 23 May 2020
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15 Oct 2021, 20:19
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (02:08) correct
34%
(02:41)
wrong
based on 180
sessions
History
Date
Time
Result
Not Attempted Yet
10 + 11 + 12 +...+ x = 5106
What is x?
A. 100
B. 101
C. 102
D. 103
E. 104
What is x?
A. 100
B. 101
C. 102
D. 103
E. 104
16 Oct 2021, 06:13
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huongguyen
Sum of first 100 terms =101*100 /2 = 5050
First 9 terms are missing = 9* 10/2 =45
Total =5050-45 =5005
in order to make it 5160 we need to add 101
Therefore IMO B
General Discussion
16 Oct 2021, 05:32
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huongguyen
Method-1:
Here are some properties that are useful for people to know.
Attachment:
Properties of sequences.png [ 106.86 KiB | Viewed 3841 times ]
Now, Sum of all the terms in any Arithmetic Progression \(= (FirstTerm+LastTerm)*(\frac{No.ofTerms}{2})\)
So, 10 + 11 + 12 +...+ x = 5106 (which has total terms = x-10+1 = x-9 terms) becomes
\(10 + 11 + 12 +...+ x = (10+x)*\frac{(x-9)}{2} = 5106\)
i.e. \((x-9)*(x+10) = 2*5106 = 2*46*111 = 92*111\)
i.e. x-9 = 92
i.e. x = 101
Method-2: USE Options
Number of terms in series 10 to x will be = x-10+1 = x-9
i.e. x-9 must be a factor of 2*5106
\(5106 = 2*3*23*37\)
Using options
A. 100 i.e. x-9 = 100-9 = 91 which is NOT factor of 2*5106
B. 101 i.e. x-9 = 101-9 = 92 = 2*2*23 which is a factor of 2*5106
C. 102 i.e. x-9 = 102-9 = 93 which is NOT factor of 2*5106
D. 103 i.e. x-9 = 103-9 = 94 which is NOT factor of 2*5106
E. 104 i.e. x-9 = 104-9 = 95 which is NOT factor of 2*5106
Answer: Option B
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Bunuel: Please shift this question to PS thread
