If for any number N, f(N) is defined as

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

If for any number N, f(N) is defined as

by Vincen » Tue Nov 21, 2017 8:16 am

If for any number N, f(N) is defined as the least integer that is greater than or equal to N^2, then f(-1.1) =

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

The OA is E.

Experts, I don't understand how f works. Can you give me some examples and then explain to me how to solve this PS question? Please.

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Source: Beat The GMAT — Problem Solving | Tue Nov 21, 2017 8:16 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Tue Nov 21, 2017 8:22 am

Vincen wrote:If for any number N, f(N) is defined as the least integer that is greater than or equal to N^2, then f(-1.1) =

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

The OA is E.

Experts, I don't understand how f works. Can you give me some examples and then explain to me how to solve this PS question? Please.

Say we had f(1.3) If f(N) is defined as the least integer that is greater than or or equal to N^2, then f(1.3) would be the least integer greater than or equal to 1.3^2, or 1.69. The least integer greater than or equal to 1.69 is 2.

Or say we had f(.5). The least integer greater than or equal to .5^2, or .25 is 1.

Effectively, we're squaring the value in parentheses and then rounding up to the nearest integer.

So if we have f(-1.1), then (-1.1)^2 will be 1.21. (It's enough to see that this value will be greater than 1 and less than 2.) The least integer greater than or equal to 1.21 is 2. The answer is E

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Tue Nov 21, 2017 11:51 am

If for any number N, f(N) is defined as the least integer that is greater than or equal to N^2, then f(-1.1) =

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

The OA is E.

Experts, I don't understand how f works. Can you give me some examples and then explain to me how to solve this PS question? Please.

Hi Vincen,
Let's take a look at your question.

The question states:
f(N) is defined as the least integer that is greater than or equal to N^2.
Therefore,
$$f\left(-1.1\right)\ =\ \left(-1.1\right)^2$$
$$f\left(-1.1\right)\ =\ 1.21$$

The least integer that is greater than or equal to 1.21 is 2.
Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 12, 2019 4:04 pm

Vincen wrote:If for any number N, f(N) is defined as the least integer that is greater than or equal to N^2, then f(-1.1) =

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

The OA is E.

Experts, I don't understand how f works. Can you give me some examples and then explain to me how to solve this PS question? Please.

Here are some examples for the values of the function f:

f(0) = 1 (since 0^2 = 0 and the least integer that is greater than or equal to 0 is 1)

f(2) = 5 (since 2^2 = 4 and the least integer that is greater than or equal to 4 is 5)

f(3/2) = 3 (since (3/2)^2 = 9/4 = 2.25 and the least integer that is greater than or equal to 2.25 is 3)

f(-7/3) = 6 (since (-7/3)^2 = 49/9 â‰ˆ 5.44 and the least integer that is greater than or equal to 5.44 is 6)

Therefore, since (-1.1)^2 = 1.21. f(-1.1) = 2 since the least integer that is greater than or equal to 1.21 is 2.

Answer: E

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