Question

The least integer of a set of consecutive even integer is
-30. If the sum of these integers is 66, how many
integers are in the set?
A) 12
B) 14
C) 30
D) 33
E) 35

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The least integer of a set of consecutive even integer is - 30. If the sum of these integers is 66, how many integers are in the set

A) 12

B) 14

C) 30

D) 33

E) 35

EVALUATION

Here it is given that the least integer of a set of consecutive even integer is - 30

So the progression is

- 30 , - 28 , - 26 , - 24 ,..

Let there are n integers such that the sum = 66

So by the given condition

$\displaystyle \sf{ \frac{n}{2} \bigg[(2 \times - 30) + (n - 1) \times 2 \bigg] = 66}$

$\displaystyle \sf{ \implies \: n \bigg[ - 30 + n - 1 \bigg] = 66}$

$\displaystyle \sf{ \implies \: n \bigg[ n - 31 \bigg] = 66}$

$\displaystyle \sf{ \implies \: {n}^{2} - 31n = 66}$

$\displaystyle \sf{ \implies \: {n}^{2} - 31n - 66 = 0}$

$\displaystyle \sf{ \implies \: {n}^{2} - 33n + 2n - 66 = 0}$

$\displaystyle \sf{ \implies \: (n - 33)(n + 2) = 0}$

$\displaystyle \sf{ \implies \: n = 33 \: ,\: \: - 2}$

Since n can not be negative

So n = 33

FINAL ANSWER

Hence the correct option is D) 33

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