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

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.

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.

Answer is A

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

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.

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]

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

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

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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