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Re: A list contains 11 consecutive integers. What is the greatest integer [#permalink]
25 Aug 2015, 00:03

Bunuel wrote:

A list contains 11 consecutive integers. What is the greatest integer on the list?

(1) If x is the smallest integer on the list, then (x + 72)^(1/3) = 4 (2) If x is the smallest integer on the list, then 1/64 = x^(-2)

Ans: A

as it is a list of consecutive int we can find the greatest if we can find the any number with its position on the list 1) Solution: (x+72) = 4^3 x+72= 64 x= -8 and x is the smallest so greatest is 2 [Sufficient] 2) 1/64 = x^-2 x^2 = 64 x= +8 and -8 two lists possible [Not Sufficient] _________________

-------------------------------------------------------------------- The Mind is Everything, What we Think we Become. Kudos will encourage many others, like me. Please Give Kudos !! Thanks

A list contains 11 consecutive integers. What is the greatest integer [#permalink]
27 Aug 2015, 22:50

2

This post received KUDOS

Given that the list contains consecutive integers, it's enough if we find one of the numbers and its position in the list to have all numbers in the list. So, if we happen to know the smallest element in the list, we also know the largest element in the list.

Let's consider statement(1)

\((x+72)^{1/3} = 4\) \(=> \sqrt[3]{(x+72)} = 4\) Cubing both sides, \(=> x + 72 = 64\) \(=> x = -8\) With this, we can also find the largest number in the list. So, A/D stands.

Re: A list contains 11 consecutive integers. What is the greatest integer [#permalink]
30 Aug 2015, 08:43

1

This post received KUDOS

Expert's post

Bunuel wrote:

A list contains 11 consecutive integers. What is the greatest integer on the list?

(1) If x is the smallest integer on the list, then (x + 72)^(1/3) = 4 (2) If x is the smallest integer on the list, then 1/64 = x^(-2)

Kudos for a correct solution.

GROCKIT OFFICIAL SOLUTION:

If we can determine the smallest integer on the list or a specific integer on the list when the list is written in increasing order, we can determine the greatest integer on the list.

1) Sufficient: We’re given one variable and one equation for the smallest integer on the list. That means we could solve for smallest integer and add 10 to find the greatest integer. If you don’t see this, consider:

\((x+72)^{\frac{1}{3}} = 4\)

Cubing both sides, x + 72 = 64. Then x + 72 = 64 and x = -8. Adding 10 to -8, the greatest integer is 2. Eliminate choices B, C and E.

2) Insufficient: If \(\frac{1}{64}=x^{-2}\) then \(\frac{1}{64}=\frac{1}{{x^2}}\) and \(x^2=64\), so x could be -8 or 8.

There are two different possibilities for the smallest integer on the list, so there must be two different possibilities for the greatest integer on the list. Statement 2) is insufficient, leaving the correct answer choice as A. _________________

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