Algebra

Hi kamalakarthi,

This is an example of a Symbolism question; these types of questions provide you with a "made up" math symbol, tell you what it "means" mathematically, then ask you to perform a calculation with it.

Here, we're told that [X] = the LEAST INTEGER that is greater than or equal to X.

In these situations, it helps to come up with some quick examples, so that you are clear on the concept:

For example:
[1] = 1
[1/2] = 1
[-2.5] = -2
Etc.

With this prompt, we're asked to figure out this…

[X] = 0

So what COULD X be so that the LEAST integer that would be greater than (or equal) X is 0?

X COULD be 0, of course.
X would have to be negative….
BUT it CAN'T be -1, since [-1] = -1

It would have be 0 and any negative fraction greater than -1

Final Answer: E

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

Rich did a great job explaining why the correct answer is E, so I won't rehash the solution.

I would, however, like to point out that this question requires us to check the answer choices. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: https://www.beatthegmat.com/mba/2014/09/ ... -questions

Cheers,
Brent

Here's a similar question in the form of a Data Sufficiency question: https://www.beatthegmat.com/clarity-need ... 67353.html

Cheers,
Brent

Hi kamalakarthi,

I provided some examples with my original post, but here's a bit more of an explanation.

In the symbol [X], the X will eventually be replaced by a number. That number could be positive, negative or 0 and it might even be a fraction or decimal.

We're told that the symbol will take whatever number is within it and perform a function (or sorts) --> the function will be to turn the number in the symbol into the LEAST INTEGER that is greater than or equal to X.

So, if….
X = 1, then [1] = 1 (since 1 is the least integer that is greater than or equal to 1.
X = 2/3, then [2/3] = 1 (since 1 is the least integer that is greater than or equal to 2/3.
X = -10.2, then [-10.2] = -10 (since -10 is the least integer that is greater than or equal to -10.2
Etc.

With your example, if…
X = 3, then [3] = 3 (since 3 is the least integer that is greater than or equal to 3.

To take things a step further, if….
[X] = 3
Then we have to think about what X could be so that the RESULT = 3.
[3] = 3
[2.5] = 3
[2.000001] = 3

So, if 2 < X <=3, then [X] = 3

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

kamalakarthi wrote:Rich/Brent,

Thank you so much for explaining this question. However I am still not able to understand the question clearly.

[X] = the LEAST INTEGER that is greater than or equal to X. What does it mean ?

Does it mean that if X =3 then does it mean all the values of x is > 3.

Another approach is to break the operation into TWO PARTS.

Example: if x = 2.6, the following INTEGERS are greater than or equal to x: 3, 4, 5, 6, ...
Of those values, 3 is the least (smallest)
So, [2.6] = 3

Example: if x = -7.3, the following INTEGERS are greater than or equal to x: -7, -6, -5, -4,...
Of those values, -7 is the least (smallest)
So, [-7.3] = -7

Example: if x = 3, the following INTEGERS are greater than or equal to x: 3, 4, 5, 6, 7,...
Of those values, 3 is the least (smallest)
So, [3] = 3

Cheers,
Brent