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Manager  Joined: 03 Jul 2013
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Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32 If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (01:56) correct 22% (02:02) wrong based on 242 sessions

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If f(a)=a^2+3a, then the value of 3f(a−b) is how many times greater than b?

1) b=3
2) a is a positive integer

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Re: If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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aadikamagic wrote:
If f(a)=a^2+3a, then the value of 3f(a−b) is how many times greater than b?

1) b=3
2) a is a positive integer

Dear Aadikamagic,

This is how you can solve it:

3f(a-b) = 3(a^2 + b^2 - 2ab + 3a - 3b)

We need to check how many time greater is this expression than b.

We can't take out b common from the equation, since we have a^2.

Now is the time to evaluate the two choices.

1. B = 3. Equating it in the equation won't help, since we know that we'll be left with a^2 + the equation with "a". Thus this alone is not going to help.

2. A is a positive integer - This will not help us since "a" can assume infinite values.

3. Putting the two together - We are left with an equation with an equation involving "a", in which "a" can assume infinite values, thus even this won't help us in giving the answer.

So, none of the two would help, neither individually not when combined together.

So Answer choice should be E
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Re: If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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Is this a gmat like question at all?
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If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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aadikamagic wrote:
If f(a)=a^2+3a, then the value of 3f(a−b) is how many times greater than b?

1) b=3
2) a is a positive integer

$$f(a)=a^2+3a$$

$$f(b)=b^2+3b$$

$$3 * f(a - b) = 3 * (a - b)^2 + 3(a - b)$$

$$3 * f(a - b) = 3 * (a^2 - 2ab + b^2 + 3a - 3b)$$

So as per the above equation in order to check if $$3f(a-b) > b$$ we would need to know the values of both a and b.

Lets check the options.

$$1) b=3$$

This gives us value of b and does not tell us anything about the value of a.

Hence, we will not be able to determine the value of $$3f(a-b) > b$$

Hence, (1) ===== is NOT SUFFICIENT

2) a is a positive integer

This does not tell us specific values of a and b.

Hence, we will not be able to determine the value of $$3f(a-b) > b$$

Hence, (2) ===== is NOT SUFFICIENT

Combining (1) & (2)

We still do not know the value of a, we only know it is a positive integer.

Hence, (1) & (2) ===== is NOT SUFFICIENT

Hence, Answer is E
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Re: If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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Simran145 wrote:
Is this a gmat like question at all?

Off course it is a GMAT Type question, why do you think so Simran145?
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Re: If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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aadikamagic wrote:
If f(a)=a^2+3a, then the value of 3f(a−b) is how many times greater than b?

1) b=3
2) a is a positive integer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

After setting up the question, we can simplify it as follows.

The question ask what the value of x is if $$3f(a-b)= 3(a-b)^2 + 3(a-b) = 3(a-b)(a-b+1) = xb$$.

There are 3 variables and 1 equation, and so we need 2 more equations to solve.
However, the condition 1) has 1 equation and the condition 2) has 0 equation.
Thus E is the answer most likely.

Condition 1) & 2)
Since $$b = 3$$ by the condition 1), we have $$3(a-b)(a-b+1) = 3(a-3)(a-2) = 3x$$.
However, we don't know the value of $$a$$, we can't find the value of $$x$$.

Therefore, E is the answer as expecteed.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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I'm confused about this question.

If you ignore the "how many times greater is b" until the end, you can get an equation that you can use the quadratic formula on which results in two answers, zero and nine. Thus, together you could know a and b and then divide the result by b.

3*((a-b)2+3(a-b)
3(a2-2ab+b2+3a-3b)
Now, plug in b = 3:
3(a2-6a+9+3a-9) = 3(a2-3a)
Using the quadratic formula, you find that a = 0 or 9
With Statement 2, you know that a = 9
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Re: If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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badgerfeet11 wrote:
I'm confused about this question.

If you ignore the "how many times greater is b" until the end, you can get an equation that you can use the quadratic formula on which results in two answers, zero and nine. Thus, together you could know a and b and then divide the result by b.

3*((a-b)2+3(a-b)
3(a2-2ab+b2+3a-3b)
Now, plug in b = 3:
3(a2-6a+9+3a-9) = 3(a2-3a)
Using the quadratic formula, you find that a = 0 or 9
With Statement 2, you know that a = 9

Hello

OK, so you have found that the value of 3f(a-b), when we put b=3, turns out to be: 3*(a^2 - 3a).
But why should we equate it to '0'. The question asks us to find 3f(a-b) is how many times greater than b?
So we divide this by b, or here we divide by '3', since first statement says that b=3. We get a^2 - 3a.

Now until we know the value of 'a' (even if we know a is a positive integer from second statement), we cannot answer this question.
Equating a^2 - 3a to 0 doesnt make any sense.

(And also just for clarification, if we equate a^2 - 3a = 0, we will get the values of a as '0' and '3', NOT 0 and 9).
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Re: If f(a)=a^2+3a, then the value of 3f(a−b)  [#permalink]

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Can someone share a list/resource of functions questions for practice? Re: If f(a)=a^2+3a, then the value of 3f(a−b)   [#permalink] 04 Aug 2019, 12:20
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