huongguyen wrote:
10 + 11 + 12 +...+ x = 5106
What is x?
A. 100
B. 101
C. 102
D. 103
E. 104
Method-1:Here are some properties that are useful for people to know.
Attachment:
Properties of sequences.png [ 106.86 KiB | Viewed 2537 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 OptionsNumber 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*5106C. 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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