In a sequence of integers, each of the m integers after the first

Question

In a sequence of integers, each of the m integers after the first integer is 5 greater than the previous integer. Thereafter, each integer is 2 less than the previous integer. If the first integer and the last integer in the sequence are each 50 and the number of integers in the sequence is 36, m = ?

A. 5
B. 15
C. 21
D. 11
E. 10

A. 5
B. 15
C. 21
D. 11
E. 10

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rajdeep212003 · Answer

What I did here was balance the total increase and total decrease.

The sequence starts at 50.

Then it increases by 5 for m integers.

After that, it starts decreasing by 2 until the last term becomes 50 again.

Since the sequence starts and ends at the same value, the total upward movement must equal the total downward movement.

So:

increase = decrease

5m = 2(35 − m)

Why 35 − m?

Because there are 36 integers total, which means there are 35 “steps” between them.

Out of those:
- m steps are +5
- remaining steps are −2

Now solving:

5m = 70 − 2m 
7m = 70 
m = 10

Answer: (E)

I found it easier to think in terms of total movement up vs total movement down instead of trying to build the whole sequence manually.

— Rajdeep

shivani1351 · Answer

I used one of the most basic AP formulae to solve this question.
Treat the sequence as two arithmetic progressions (APs), as they have fixed differences involved.

For the 1st AP (increasing by 5), using the AP formula nth term = a+(n-1)d:
Peak term = 50+(m+1-1)(5) = 50+5m
The value of n here is m+1 because it is given that there are m integers after the first integer (pay attention to the keyword 'after' here)

For the 2nd AP (decreasing by 5), using the same AP formula again:
In this AP, the first term is 50+5m (the peak term), last term = 50 (given in the question) and the common difference = -2 (given in the question).

Let number of terms in this decreasing part be k. Thus,
50 = 50+5m+(k-1)(-2)
Simplifying, we get: k = (5m+2)/2

Since the total number of terms given in the AP = 36:
=> (m+1)+k-1 = 36
=> m+k = 36

Reasoning:
Increasing AP has m+1 terms
Decreasing AP has k terms (including the peak term)
But the peak term gets counted twice, hence accounted for the same by -1 in the above equation.

Now, we have m+k = 36 and k = (5m+2)/2:
m + (5m+2)/2 = 36
Solving for the value of m, we get m = 10

Hence, the correct answer is Option E - 10.

Hope this helps!

ExpertsGlobal5 · Answer

E is the correct answer choice.

Video explanation:

https://www.youtube.com/watch?v=IZJdCu7teCI

hasanovaci · Answer

i solved it looking at the answers where E is the only even integer which could be possible answer.

odd integers can not be true as 50 + 5*odd = odd. and odd - 2*any integer = even (50) is not possible.

In a sequence of integers, each of the m integers after the first

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GMAT Problem Solving (PS) Questions

In a sequence of integers, each of the m integers after the first

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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