On the number line above, p, q, r, s, and t are five consec

Hi All,

This DS question is full of Number Properties and the math involved is fairly straight-forward. However, if you don't see the "elegant" approach to answer this question, then you can still use "brute force" and some basic Arithmetic to get the correct answer.

We're given a number line with 5 variables on it. We're told that the variables represent 5 CONSECUTIVE EVEN INTEGERS. That's a very specific set of "restrictions", so you can use them to your advantage if you have to "play around" with this question. We're asked for the AVERAGE of the 5 integers. Since we know that they're consecutive evens, if we can figure out ANY of them, then we can figure out the others AND answer the question.

Fact 1: Q + S = 24

Looking at the drawing, we know that Q, R and S are 3 CONSECUTIVE EVEN INTEGERS, so even if we don't know how to do the Algebra here, we can still run some TESTs....

IF Q, R and S are....
2, 4 and 6, then Q+S = 8. That's too small though (it's supposed to be 24)

IF Q, R and S are a bit bigger, say....
8, 10 and 12, then Q + S = 20. This is still too small, but it's getting closer to 24...

IF Q, R and S are....
10, 12 and 14, then Q + S = 24. This is a MATCH for what we're looking for. We can also figure out the missing values (they're 8 and 16).

By making these variables larger or smaller, the sum of Q+S won't = 24, so we know that the 10/12/14 example is the ONLY possibility that fits.
Fact 1 is SUFFICIENT.

Fact 2: The average of Q and R is 11

Since Q and R are 2 CONSECUTIVE EVEN INTEGERS, we're going to need 2 numbers that are close to 11....

IF Q and R are....
8 and 10, then the average is 9 (which is not a match; it's supposed to be 11)

IF Q and R are...
10 and 12, then the average is 11. This is a MATCH.

Making Q and R any bigger will raise the average (and it won't match), so we know that 10 and 12 are the ONLY possible values that fit. The other numbers would be 8, 14 and 16.
Fact 2 is SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

We are not told that p, q, r, s, and t are consecutive integers. We are given that p, q, r, s, and t are five consecutive EVEN integers. For example 2, 4, 6, 8, 10.

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 five integers?

(1) q + s =24

As we know that r is the median of q and s, and r is also the median of p,q,r,s, and t. Hence, if we know the value of r we should be able to answer the question.

q + s = 24

Midpoint = 24/2 = 12 = r

Hence, (1) ===== is SUFFICIENT

(2) The average (arithmetic mean) of q and r is 11

q = r - 2

r - 2 + r = 11 * 2

2r = 24

r = 12

Hence, (2) ===== is SUFFICIENT

Hence, Answer is D

Did you like the answer? Hit Kudos

Ans. : Let p=x, q=x+2, r=x+4 , s=x+6, t=x+8 to find the mean we need to find x.
From statement 1 , we get 2x+8=24
From statement 2 we get x+3=11
Therefore the answer is (D).

Solution:

Recall that in a set of evenly spaced numbers, mean is equal to the median. Thus, the average of these five integers is equal to r.

Statement One Alone:

q + s = 24

Notice that the set consisting of q, r and s is also evenly spaced; therefore the mean of this set is also equal to the median, which is r. Recall that for a set of evenly spaced numbers, the mean is equal to the average of the greatest and the smallest elements; thus r = mean = (q + s)/2 = 24/2 = 12.

Statement one alone is sufficient.

Statement Two Alone:

The average of q and r is 11.

Since (q + r)/2 = 11, q + r = 22. Since q and r are consecutive even integers, q = r - 2. Then, (r - 2) + r = 2r - 2 = 22. Solving the equation, we get r = 12.

Statement two alone is sufficient.

Answer: D

My understanding of consecutive integers, is that they are separated by only 1, i.e. 3, 4, 5, 6, 7, 8

I was able to find the first statement sufficient, but not the second, mainly because the answer uses the formula p + (p+2) +....

Why is 2 being added to P?

Updated - Thank you for bring it up.
Thanks__

which is the level of the question? 500? tks a lot

I'd say it's ~600.

P.S. You can see the difficulty level of a question in the first post where the tags are (TAGS: Difficulty: 600-700 Level).

They are basically giving us some equation in disguise.

1. q+s=24 but for a fact set we know that the leap between q and s is 4 and this translates into an equation that subtracted gives us the value of q from which we can calculate the average.
2. q+r=22 same old story, the leap between q and r this time is 2 units. r-q=2 subtract it from the given equation and you are done you got one value, the remaining values follow logically.

D.

Given:
CONSECUTIVE EVEN INTEGERS
p=2n
q=2n+2
r=2n+4
s=2n+6
t=2n+8

p<q<r<s<t

Mean= (2n+2n+2+2n+4+2n+6+2n+8)/5
= (10n+20)/5
=10(n+2)/5
=2(n+2)


(1) q+s=24
2n+2+2n+6=24
One variable thus can be solved.

Sufficient.

AD

(2) Mean= (2n+2+2n+4)/2

One variable thus can be solved.

D

STatement 1 no. of terms is 5 so the center term i.e r will be the avg as the series is an Arithmetic progression
so it can be found by (q +s)/2 = 12.

Statement 2 : given :- (q + r) / 2 = 11.
also q = r-2 (as all are even consecutive integers in a series.)
So again the avg can be found out.

Answer D

1) q+s=24
p,q,r,s,t

s-q= 4 and s+q =24. add them. s=14 and series will be 8,10,12,14,16 and mean will be 12. sufficient A/D can be answer

2) mean of q and r is 11, q+r=22.
r+q=22 , r-q =2 add them r=12, and series will be again same and same answer as above therefore sufficient

D is answer

P, Q, R, S, and T are consecutive even integer. Let p = X, So,
P = X
Q=X+2
R=X+2+2=X+4
S= X+4+2=X+6
T=X+6+2=X+8

(1) X+2+X+6=24 Sufficient to the value of X; Sufficient.

(2) [(x+2+x+40/2]=11; We will get the value of x from this equation. Sufficient.

Answer D.

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question. We have to find an average of five integers.

=> p, q, r, s and t are consecutive even integers.Therefore,

=> q = p + 2, r = p + 4, s = p + 6 and t = p + 8.

=> We need value of \(\frac{(p + p + 2 + p + 4 + p + 6 + p + 8) }{ 5}\) OR \(\frac{(p + 20)}{5}\)

Second and the third step of Variable Approach: From the original condition, we have 1 variable (p).To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Let’s take look at each condition.

Condition(1) tells us that the q + s = 24.

=> p + 2 + p + 6 = 24

=> 2p = 16 or p = 8

=> Average: \(\frac{(8 + 20) }{ 5}\) = 5.6

Since the answer is unique, condition(1) alone is sufficient by CMT 2.


Condition(2) tells us that the average mean of 'q' and 'r' is 11 .

=> q + r = 11 * 2 = 22

=> p + 2 + p + 4 = 22

=> 2p = 16 or p = 8

=> Average: \(\frac{(8 + 20) }{ 5}\) = 5.6

Since the answer is unique, condition(2) alone is sufficient by CMT 2.


Each condition alone is sufficient.

So, C is the correct answer.

Answer: C

Since, it is a key question[Statistics], if value of Con(1) = value of Con(2), answer is D

Answer: Option D

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