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Difficulty:
25%
(medium)
Question Stats:
77% (01:42) correct
23%
(02:01)
wrong
based on 293
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If x ? y is defined for all x and y as the sum of all integers from x to y, inclusive, what is the value of 5 ? 150?
A. 22,630
B. 22,475
C. 11,315
D. 11,238
E. 5,658
A. 22,630
B. 22,475
C. 11,315
D. 11,238
E. 5,658
x ? y = the sum of all integers from x to y, inclusive
Find : 5 ? 150
5 ? 150 = 5+6+7...+150
Sum of Continues series a+(a+1)+(a+2)+.... L = S = \(\frac{n}{2} *(a+L)\)
where n is number of terms, a is first term, L is last term
Here number of terms = (150-5)+1 = 146 ( Here +1 as 150 and 5 both are included)
Sum=\(\frac{146}{2}* (5+150) = \frac{146}{2} *(155)\)
= 11315
Answer: C
Find : 5 ? 150
5 ? 150 = 5+6+7...+150
Sum of Continues series a+(a+1)+(a+2)+.... L = S = \(\frac{n}{2} *(a+L)\)
where n is number of terms, a is first term, L is last term
Here number of terms = (150-5)+1 = 146 ( Here +1 as 150 and 5 both are included)
Sum=\(\frac{146}{2}* (5+150) = \frac{146}{2} *(155)\)
= 11315
Answer: C
Bunuel
The ? strange symbol just gives the rule that, in this problem, the task is to find the sum of an arithmetic series of integers, from 5 to 150 inclusive.
Sum = (Average) * (Number of terms)
Average = \(\frac{First Term + Last Term}{2}\)
Average = \(\frac{150 + 5}{2}\) = \(\frac{155}{2}\) Leave it.*
Number of terms = (Last Term - First term + 1)
Number of terms = (150 - 5) + 1 = 146
Sum of series: \(\frac{155}{2}\) * (146) = 155 * 73
If you do the arithmetic fully, 155 * 73 = 11,315
ANSWER C
To simplify the arithmetic:
Three answers, A, D,and E, can be eliminated immediately because the units' digit of the answer must be five (3*5 = 15).
Between B and C: Answers B and C are far enough apart that you can round numbers to speed the arithmetic.
150 * 70 = 10,500. That's close to C. To get close to Answer B, the number of terms would have to double.
Either way:
Answer C
*If the average of consecutive integers is not an integer because the sum of the first and last terms is odd (odd/2 = not integer), the number of terms will be even, and the 2 in the denominator will be factored out. So write the two factors, average and number of terms, before calculating; that way it is clear that dividing by 2 will lead to an integer.
