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

Question

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)^{(\frac{1}{3})} = 4

(2) If x is the smallest integer on the list, then  \frac{1}{64} = x^{(-2)}

Kudos for a correct  solution .

SOURH7WK · Answer

Answer A)
Statement 1 will have unique value of x ie -8
Statement 2 will have 2 values of x ie +8 & -8

D3N0 · Answer

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  
2) 1/64 = x^-2 
x^2 = 64
x= +8 and -8 
two lists possible

scorpionkapoor77 · Answer

As answered above, In order to find the greatest integer, we need to find the value of x.

(1) provides single value of x. Enough
(2) provides two values of x. Not enough

Hence, A is the answer.

VenoMfTw · Answer

IMO : A

St 1:
 (x + 72)^(1/3) = 4 
Cubing on both sides
 (x + 72)= 4^3 
x=-8
Suff

St 2:
1/64 = x^(-2)
x = 8 or -8 
Not suff

lipsi18 · Answer

1. (x+72) ^1/3 = 4 ; cubing both the side; (x+72)=64 => x=-8; so we will be able to get answer.

2. 1/64 = 1/x^2 ; x = -8, +8; therefore not sufficient to answer the question.

Hence answer is A

hiteshahire22 · Answer

Correct Answer A.

A - X can be obtained by Simple math as a fixed value -8
Therefore, the series will be unique (-8,-7,-6,...0,1,2)
Hence it's Sufficient.

B - The Value of X obtained is +/- 8.
Hence, the series will not be unique (Two different series 8, 9, 10,......18 or -8,-7,-6,.....2) 
Not sufficient.

rajarams · Answer

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 {(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.

Consider (2)

1/64 = x^{-2} 
 => 1/64 = 1/x^2 
 => x^2 = 64 
 => x = \pm8

We have two values for x here and hence the greatest element in the list can vary based on this.
Hence, A

AvengerGmat · Answer

Answer is A

1) solving 1 x=-8
2) solving 2 x=+8 and -8

Bunuel · Answer

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 .

jasimuddin · Answer

1) (x+72)^1/3 =4
 or, x+72 = 4^3 = 64
 or, x=- 8...so sufficient
2) 1/64 = x^-2
 x= 8 or -8 ....insufficient
ans: A

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

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

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