Question

P, Q, R, S, and T are 5 consecutive even numbers. If the sum of P and S is 150, what is the sum of all the numbers?​

Answer 1

P = P

Q = P + 2

R = P + 4

S = P + 6

And T = P + 8

According to question: P + S = 150

P + P + 6 = 150

2P = 144

P = 72

=> Sum of all numbers = P + Q + R + S + T = 72 + 74 + 76 + 78 + 80

=> = 380

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Answer 2

$\huge \orange \star \pink{answer : }$

We're told that P, Q, R, S and T are five CONSECUTIVE EVEN integers in INCREASING order. We're asked for the average (arithmetic mean) of the 5 integers. This question can be solved with a bit of logic and some 'brute force' Arithmetic.

To start, it helps to think in terms of what is described: without any additional information, the 5 numbers could be 0, 2, 4, 6, 8 or 4, 6, 8, 10, 12 for example (they could even potentially include some negative values). You might find it helpful to note that the largest number in the group will be exactly 8 more than the smallest number in the group.

1) Q + S = 24

With this Fact, you could 'brute force' the solution (plug in sequences of 5 consecutive even integers until you find the one that 'fits'), or you could use the prior deduction to your advantage (the biggest number is 8 more than the smallest). Either way, there's ONLY ONE solution: Q = 8 and S = 16... meaning that the 5 numbers are 8, 10, 12, 14 and 16. You know that you CAN calculate the exact average - so you don't need to do any more work.

Fact 1 is SUFFICIENT

2) The average (arithmetic mean) of Q and R is 11.

Since we know that Q and R are CONSECUTIVE EVEN integers, the fact that they have an average of 11 means that there's ONLY ONE possible solution (Q = 10 and R = 12). This leads to the same group of 5 integers we defined in Fact 1: 8, 10, 12, 14 and 16. You know that you CAN calculate the exact average - so you don't need to do any more work.

Fact 2 is SUFFICIENT

Final Answer: D