vikkimba17 wrote:In a decreasing sequence of seven consecutive even integers, the sum of the first four integers is 68. What is the product of the last three integers in the sequence?

A)1,000
B)960
C)925
D)30
E)25

Hi vikkimba17,

We have a decreasing sequence of seven consecutive even integers.

Since the sum of the first four integers is 68, the average of them = 68/4 = 17. '17' is the integer that lies between the 6th and the 5th integer. Thus, the 5th integer would be 17 - 1 = 16 and the 6th one would be 17 + 1 = 18. Since the sequence of seven numbers is a sequence of consecutive even integers, the decreasing sequence would be: 20, 18, 16, 14, 12, 10, 8.

The product of the last three integers in the sequence = 12*10*8 = 960.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Number Properties Guide

-Jay
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vikkimba17 wrote:In a decreasing sequence of seven consecutive even integers, the sum of the first four integers is 68. What is the product of the last three integers in the sequence?

A)1,000
B)960
C)925
D)30
E)25

We can also solve the question algebraically.

In a decreasing sequence of seven consecutive even integers....
Let x = the 1st number
So, x-2 = the 2nd number (since we have descending EVEN integer)
And x-4 = the 3rd number
And x-6 = the 4th number
And x-8 = the 5th number
And x-10 = the 6th number
And x-12 = the 7th number

...the sum of the first four integers is 68
We get: x + (x-2) + (x-4) + (x-6) = 68
Simplify: 4x - 12 = 68
Solve: x = 20
So, the 1st number is 20, which means all 7 numbers are 20, 18, 16, 14, 12, 10, 8

What is the product of the last three integers in the sequence?
(12)(10)(8) = 960

Answer: B

Cheers,
Brent

Hi vikkimba17,

There are some built-in Number Properties in this question that we can take advantage of. To start, since we're taking the product of 3 CONSECUTIVE EVEN integers, the product MUST be even - so we can eliminate Answers C and E immediately.

Next, we can think in terms of the what the product COULD be (regardless of the what the first 4 integers in the sequence were). Since the remaining three answers all end in a 0, one of the three even integers MUST be 10....

(10)(8)(6) = 480

Notice how that's exactly HALF of one of the answers. What if we changed the 6 into a 12...

(12)(10)(8) = 960

That's a match for one of the options; and since Answer A isn't a product that we can get to with 3 consecutive evens, 960 MUST be the answer.

Final Answer: B

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