Equations & Functions

[sparkle6]

Find the value of 'a' if a(x^3) + 9(x^2) + 4x - 10 when divided by (x+3) leaves a remainder of 10.

a. -2
b. -1
c. 0
d. 1
e. 2

[Brent@GMATPrepNow]

Find the value of 'a' if a(x^3) + 9(x^2) + 4x - 10 when divided by (x+3) leaves a remainder of 10.
a. -2
b. -1
c. 0
d. 1
e. 2

Holy out-of-scope, Batman

This question requires knowledge of the Remainder Theorem - definitely not required knowledge for the GMAT.

Cheers,
Brent

[chetansharma]

@Sparkle6,
Is the question correct?? If so, what is the OA?

@Brent,
I have tried solving the question using the synthetic division method, but not able to get the answer. Please check the solution below and let me know where I am going wrong. (Though this question is out of scope, I tried solving the question as the soln requires only high school standard mathematics. But I am not able to do so )

-3| a 9 4 -10
| -3a 9a-27 -27a+69
-------------------------------
a -3a+9 9a-23 -27a+59

As the remainder is stated as 10, -27a+59 = 10 => a= 49/27 : :roll:

Please let me know, where am I going wrong.

Regards
Chetan
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[Brent@GMATPrepNow]

@Brent,
I have tried solving the question using the synthetic division method, but not able to get the answer. Please check the solution below and let me know where I am going wrong. (Though this question is out of scope, I tried solving the question as the soln requires only high school standard mathematics. But I am not able to do so )

-3| a 9 4 -10
| -3a 9a-27 -27a+69
-------------------------------
a -3a+9 9a-23 -27a+59

As the remainder is stated as 10, -27a+59 = 10 => a= 49/27 : :roll:

Please let me know, where am I going wrong.

Yes, this is definitely a high-school-level question, but still out of scope GMAT-wise.

Nevertheless, let's solve the question.

The Remainder Theorem says something like: If f(x) divided by x-k leaves a remainder of z, then f(k) = z

So, we are told that f(x) = a(x^3) + 9(x^2) + 4x - 10, and we are told that f(x) divided by x+3 leaves a remainder of 10.

The Remainder Theorem tells us that f(-3) must equal 10

When we plug x = -3 into the function we get:
a(-3)^3 + 9(-3)^2 + 4(-3) - 10 = 10
Simplifying, we get -27a + 81 - 12 - 10 = 10
Simplifying more: -27a = -49
So, a = 49/27

Cheers,
Brent

[chetansharma]

@Brent,
I have tried solving the question using the synthetic division method, but not able to get the answer. Please check the solution below and let me know where I am going wrong. (Though this question is out of scope, I tried solving the question as the soln requires only high school standard mathematics. But I am not able to do so )

-3| a 9 4 -10
| -3a 9a-27 -27a+69
-------------------------------
a -3a+9 9a-23 -27a+59

As the remainder is stated as 10, -27a+59 = 10 => a= 49/27 : :roll:

Please let me know, where am I going wrong.

Yes, this is definitely a high-school-level question, but still out of scope GMAT-wise.

Nevertheless, let's solve the question.

The Remainder Theorem says something like: If f(x) divided by x-k leaves a remainder of z, then f(k) = z

So, we are told that f(x) = a(x^3) + 9(x^2) + 4x - 10, and we are told that f(x) divided by x+3 leaves a remainder of 10.

The Remainder Theorem tells us that f(-3) must equal 10

When we plug x = -3 into the function we get:
a(-3)^3 + 9(-3)^2 + 4(-3) - 10 = 10
Simplifying, we get -27a + 81 - 12 - 10 = 10
Simplifying more: -27a = -49
So, a = 49/27

Cheers,
Brent

So I have solved it correctly
I have rechecked my soln so many times as I was not arriving at the answer.
Thanks Brent for confirming my answer.

Regards,
Chetan

_________________
If my post helped you - let me know by pushing the thanks button

[saketk]

Brent - again, this is a CAT (common admission test) type of question.. this exam is held for admission in IIMs (indian institute of management ) -


the options given are also incorrect. - though this one is simple but I guess we need a Beat the CAT for these questions.

[Brent@GMATPrepNow]

Brent - again, this is a CAT (common admission test) type of question.. this exam is held for admission in IIMs (indian institute of management ) -

the options given are also incorrect. - though this one is simple but I guess we need a Beat the CAT for these questions.

I agree 100%.

This happens to be one of my beefs: when out-of-scope questions are posted on this webiste, they only serve to frustrate/intimidate/frighten students who are interested in learning only what is required to conquer the GMAT.

I won't go on any further, since I've already elaborated on this beef in previous posts

Cheers,
Brent