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

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Bunuel
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If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   06 May 2020, 02:17
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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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E
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Re: If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   Updated on: 06 May 2020, 02:55
f(a) = a*(a+3)

Q. The value of 3f(a − b) is how many times greater than b?

(1) b = 3

3f(a − 3) = 3*(a-3)*(a) = k.b = k.3
We don't know the value of a
Thus we cannot deduce k value or how many times greater than b the value of 3f(a − b) is
NOT SUFFICIENT

(2) a is a positive integer

We don't know the exact value of a and b. Thus we cannot deduce how many times greater than b the value of 3f(a − b) is
NOT SUFFICIENT

Combined

We don't know the exact value of a. Thus we still cannot deduce how many times greater than b the value of 3f(a − b) is
NOT SUFFICIENT

FINAL ANSWER IS (E)
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Originally posted by freedom128 on 06 May 2020, 02:49.
Last edited by freedom128 on 06 May 2020, 02:55, edited 1 time in total.
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Re: If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   06 May 2020, 02:55
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Clearly (1) is required bro even comment about 'b'

f(a-b) = (a-3)^2 + 3(a-3) = a^2-6a+9+3a-9 = a^2-3a

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

Considering (2), for a</=2, 3f(a-b) < b, for a>/=3, 3f(a-b)>b. Hence, this as well is inadequate to conclude that 3f(a-b) > b.

Answer (E).

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Re: If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   06 May 2020, 04:45
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If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times greater than b?
\(3f(a − b) = 3*[(a-b)^2 + 3(a-b)] = 3*[a^2 + b^2 - 2ab +3a - 3b]\)
\(3f(a - b) = 3*[f(a) + b^2 -2ab - 3b]\)
To find: \(\frac{3f(a - b)}{b} = 3*\frac{[f(a) + b^2 -2ab - 3b]}{b}\)
Hence we need values of both a and b.

(1) b = 3
INSUFFICIENT.

(2) a is a positive integer
INSUFFICIENT.

Together 1 and 2
a = ? and b = 3

INSUFFICIENT.

Answer E.
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Re: If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   06 May 2020, 12:57
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Quote:
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


(1) insufic
3[(a-b)^2+3(a-b)]/b=3[a^2+b^2-2ab+3a-3b]/b

(2) insufic

(1/2) insufic
3[(a-3)^2+3(a-3)]/3=[x^2-3x], x=?!

ans (E)
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Re: If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   06 May 2020, 16:47
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If f(a) = \(a^2 + 3a\), then the value of \(3f(a − b)\) is how many times greater than \(b\)?

\(3f(a − b) = 3( (a-b)^{2} +3(a-b)= 3 (a-b)(a-b+3)\)

---> \(\frac{3 (a-b)(a-b+3)}{b}\)= ???

(Statement1): b = 3
\(\frac{3(a-3)(a-3+3)}{3}= a(a-3)\)
--> NO info about what a is
Insufficient

(Statement2): a is a positive integer
No info about what b is.
Insufficient

Taken together 1 &2,
a could be any positive integer
--> if a =4, then 4(4-3)= 4 times greater than b
--> if a= 5, then 5(5-3)= 10 times greater than b
Insufficient

Answer (E).
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Re: If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   06 May 2020, 21:08
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
stem:
3f(a-b)=3(a-b)(a-b+3)
1) 3(a-3)(a) => 3(a^2-3a) [ a value not known]
insufficient
2) b value not known
insufficent
1+2,
insufficient [a value not known]
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Re: If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   26 May 2020, 02:30
If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times greater than b?

(1) b = 3, - Insufficient - Value of A is unknown.

(2) a is a positive integer - Insufficient - B is unknown.

C - Insufficient. If a = 3, 3f( 3 - 3 ) = 0, would have different value than a = 5.

Answer - E
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If f(a) = a^2 + 3a, then the value of 3f(a − b) is how many times grea [#permalink] New post   02 Dec 2020, 14:13
Bunuel wrote:

Competition Mode Question



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


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


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

\(3f(a-b) = 3a^2 + 3b^2 - 6ab + 9a - 9b\)

How many times is \(3a^2 + 3b^2 - 6ab + 9a - 9b\) greater than \(b\)? We would need to know the values of a and b to answer the question.

(1) Gives us b; no information about a. INSUFFICIENT.

(2) Tells us a is positive; no information about b. INSUFFICIENT.

(1&2) We need the exact value of a. Combined, we still can't determine the answer. INSUFFICIENT.

Answer is E.
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Re: If f(a) = a^2 + 3a, then the value of 3f(a b) is how many times grea [#permalink] New post   14 Oct 2022, 09:45
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Re: If f(a) = a^2 + 3a, then the value of 3f(a b) is how many times grea [#permalink]
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