khushboo143 wrote:n is the product of least and greatest 6 consecutive integers.what is n?
1)the greatest integer is 20
2)the average arithmethic mean of 6 consecutive integers is 17.5
ans is D..each satisfy the condition
Please post the exact wording of the question; words like "of" and "the" make a huge difference in interpretation.
I'll use my GMAT decoder ring to restate what was probably the actual question:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n?
What do we know? That we have a list of 6 consecutive integers. So, if we can determine which integers make up our list, we can certainly answer the question.
(1) the greatest integer in the list is 20
Well, if we know the biggest number on the list we can certainly count backwards to determine the other 5: sufficient.
(2) the average (arithmetic mean) of the integers is 17.5
Since our numbers are consecutive, we can certainly use this information to figure out exactly what the list is: sufficient.
If we needed to actually do so, we could:
1) know that for a set of consecutive numbers, mean = median. Since we have an even number of terms, the median is the average of the two middle terms, so the two middle terms in our set must be 17 and 18, which we can then expand to {15, 16, 17, 18, 19, 20}; or
2) use the average formula.
Average = (sum of terms)/(# of terms)
17.5 = (t1 + t2 + t3 + t4 + t5 + t6)/6
105 = t1 + t2 + t3 + t4 + t5 + t6
And, since our terms are consecutive, we know that:
t1 + t2 + t3 + t4 + t5 + t6 = t1 + (t1 + 1) + (t1 + 2) + (t1 + 3) + (t1 + 4) + (t1 + 5)
so
105 = 6(t1) + 15
90 = 6(t1)
15 = t1
so our set must be {15, 16, 17, 18, 19, 20}
Lots of other tricks we could use to also figure out the exact set.
Each of (1) and (2) is sufficient alone: choose D.
