p,q,r,s and t are five consecutive even integers

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 am; Thanked: 20 times; Followed by:1 members

p,q,r,s and t are five consecutive even integers

by bhumika.k.shah » Tue Feb 09, 2010 9:47 am

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Hi , i needed to know different approaches to solve this problem. Since i couldnt find it posted previously on btg i thought of posting it as a new topic.

Though i got OGs explanation i wanted to know various approaches it can be solved in, If any .

p q r s t

93. On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these fi ve integers?

(1) q + s = 24
(2) The average (arithmetic mean) of q and r is 11.

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Source: Beat The GMAT — Data Sufficiency | Tue Feb 09, 2010 9:47 am

outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 am; Thanked: 46 times; Followed by:3 members

by outreach » Tue Feb 09, 2010 10:16 am

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a)
q+s=24
now p, q, r, s, and t are five consecutive even integers
q=10 and s=14 satisfies the requirement

sufficient

b)
(q+r)/2=11
q+r=22
now p, q, r, s, and t are five consecutive even integers
q=10 and r=12 satisfies the requirement

sufficient

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

by thephoenix » Tue Feb 09, 2010 10:27 am

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we know that
q=p+2
r=p+4,s=p+6,t=p+g8

we are given one eqn and we need to know one variable in order to find the avg

1)hence one eqn---one variable is suff

2) same one eqn one variable...suff

another appraoch
q+s=p+2+p+6=24 solving p=8
series=8,10,12,14,16 avg=12
suff

q+r=q+q+2=11*2--->q=10

therefore ser=8,10,12,14,16
avg=12
suff

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by [email protected] » Sun Apr 01, 2018 7:54 pm

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Hi All,

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

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