GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2019, 13:21 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which of the following function follows the rule: f(a + b) = f(a)*f(b)

Author Message
TAGS:

### Hide Tags

Manager  G
Joined: 10 Mar 2019
Posts: 75
Location: Russian Federation
Schools: Booth, Berkeley Haas
GMAT 1: 730 Q50 V39 GPA: 3.95
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

2
The correct answer is E, because

24^(a+b)=(24^a)*(24^b)
24^(a+b)= 24^(a+b)
Intern  B
Joined: 26 May 2018
Posts: 45
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

2
A=2; b=3; a+b=5

e) f(x)=24x
24ˆ5= 24ˆ2+24ˆ3=2+3=5
Director  P
Joined: 04 Sep 2015
Posts: 665
Location: India
WE: Information Technology (Computer Software)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
IMO E

1: let x=1,b=2
f(a+b)=(1+2)^2+1=10,
f(a)+f(b)=(1+1)+( 4+1)=7 so this option is wrong

2:let a=0 and b=1
(5^2(1))/3 not eqaul to (5^2(0))/3 + (5^2(1))/3
wrong

3: let a=0 and b=1
(3(0)+2)+(3(1)+2)=7
and 3(1)+2=5
and so this option is also wrong

4:let a=1 and b=2
root(2(1))+root(2(2))=2+root(2)
root(2)(3)=root(6)

so f(a+b) not equal to f(a)+(b) and this option is wrong for this reason.

5:let a=1 and b=2
(24)^(3)=24^1*24^2

Option E is the correct answer.
Manager  G
Joined: 30 May 2019
Posts: 109
Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Answer is E. For such questions, I try to plug in values. a=5, b=5.
Only E will yield the same result in both sides. 24^10=$$24^5$$*$$24^5$$=24^10=24^10(5+5). Even if a is 3, and b is 7, $$24^3$$*$$24^7$$=24^3+7=24^10

Originally posted by mira93 on 08 Jul 2019, 08:54.
Last edited by mira93 on 08 Jul 2019, 22:51, edited 4 times in total.
Manager  G
Joined: 30 Nov 2017
Posts: 194
WE: Consulting (Consulting)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

Posted from my mobile device
_________________
Be Braver, you cannot cross a chasm in two small jumps...
Intern  B
Joined: 17 Jul 2018
Posts: 8
GMAT 1: 630 Q50 V25 GMAT 2: 660 Q49 V31 Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
IMO E

Assume values a=2 and b=3
Hence, f(5) = f(2)*f(3)

Now, substitute x=2,3 and 5 in all the options.
Only for option E, LHS = RHS.

f(2) = 24^2
f(3) = 24^3
f(5) = 24^5

Hence, f(2)*f(3) = 24^2*24^3 = 24^5 = f(5)
Intern  B
Joined: 26 May 2019
Posts: 3
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

2
by just looking at equations and substituiting
2and 3 for a& b

24^5=24^2*24^3=24^(2+3)

option E
Senior Manager  P
Joined: 10 Jan 2017
Posts: 330
Location: India
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Correct option is E
Attachments

File comment: Solution : IMG_20190708_212959.JPG [ 1.06 MiB | Viewed 289 times ]

Manager  S
Joined: 18 Feb 2017
Posts: 93
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
IMO E.

f(a+b)=f(a)∗f(b).
Let's consider a=2 and b=3 for all the options.

1. f(x)=x^2+1
f(2)= 5 and f(3) = 10. f(2+3)= 26 =/= 50. Incorrect option.

2. f(x)=5^(2x)/3
f(2)= 5^(4)/3 and f(3)= 5^(6x)/3. f(5) = 5^(10x)/3 =/= 5^(10x)/9. Incorrect option.

3. f(x)=3x+2
f(2)= 8, f(3)= 11, f(5)=17 =/= 88. Incorrect option.

4. f(x)=√2x
f(2)= 2, f(3)= √6, f(5)= √10 =/= 2√6. Incorrect option.

5. f(x)=24^x.
f(2) =24^2 , f(3)=24^3, f(5) = 24^5 ==24^5. Correct option. .
Manager  G
Joined: 08 Jan 2018
Posts: 145
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
IMO-E

Rule: f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b)?

Pre Thinking- For fn f(x)=a^x , f(a+b)=f(a)*f(b)..A/c Ans E

However , if we don't know that lets try by putting values.
Assume a=1, b=2

A. f(x)=x^2+1
f(2)=5, f(3)=10, f(2+3)=26
Clearly, f(2+3)=26 not equals f(1)*f(2)=50

B. f(x)=5^2x/3
f(3)=5^6/3, f(2)=5^4/3, f(2+3)=5^10/3
Clearly, f(2+3)=5^10/3 not equals f(1)*f(2)=5^10/9

Similarly for C & D , f(2+3) not = f(2)*f(3)

E.f(x)=24^x
f(2)=24^2, f(2)=24^3, f(2+3)=24^5
f(2+3) = f(2)*f(3)
SVP  D
Joined: 03 Jun 2019
Posts: 1880
Location: India
Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)

$$A. f(x)=x^2+1$$
$$f(a+b)= (a+b)^2+1$$
$$f(a)= a^2+1$$
$$f(b)= b^2+1$$
$$f(a).f(b)= (a^2+1)(b^2+1)$$
f(a+b)<>f(a).f(b)

B. f(x)=5^2x/3
f(a+b)= 5^2(a+b)/3
f(a)= 5^2a/3
f(b)=5^2b/3
f(a).f(b)= 5^2(a+b)/9
f(a+b)<>f(a).f(b)

C. f(x)=3x+2
f(a+b)= 3(a+b)+2 = 3a+3b+2
f(a)= 3a+2
f(b)= 3b+2
f(a).f(b)= (3a+2)(3b+2) = 9ab+6b+6a+4
f(a+b)<>f(a).f(b)

$$D. f(x)=\sqrt{2x}$$
$$f(a+b)= \sqrt{2(a+b)}$$
$$f(a)=\sqrt{2a}$$
$$f(b)=\sqrt{2b}$$
$$f(a).f(b)=2\sqrt{ab}$$
f(a+b)<>f(a).f(b)

E. f(x)=24^x
f(a+b)=24^(a+b)
f(a)=24^a
f(b)=24^b
f(a).f(b)=24^a.24^b = 24^(a+b) = f(a+b)

IMO E

Originally posted by Kinshook on 08 Jul 2019, 09:15.
Last edited by Kinshook on 08 Jul 2019, 09:21, edited 2 times in total.
Manager  G
Joined: 28 Feb 2014
Posts: 209
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
A. f(x)=x^2+1
(a+b)^2+1 is not equal to (a^2+1)(b^2+1)

B. f(x)=(5^2x) /3
(5^2(a+b)) /3 is not equal to (5^2a) /3 * (5^2b) /3

C. f(x)=3x+2
3(a+b)+2 is not equal to (3a+2)(3b+2)

D. f(x)=√2x
√2(a+b) is not equal to √2a*√2b

E. f(x)=24^x
24^(a+b) = 24^a*24^b (as we know when bases are same powers gets added)

E is correct
Intern  B
Joined: 02 Mar 2016
Posts: 18
Concentration: Technology, General Management
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Hit and try in options in E 24^x * 24*y = 24 (x+y)
Intern  S
Joined: 17 Aug 2016
Posts: 39
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
f(a+b)= f(a) ∗ f(b)

Using option (e)

$$24^(a+b)$$= $$24^a$$ * $$24^b$$. which satisfies.

IMO. (e) is the right answer.
Intern  B
Joined: 08 Nov 2016
Posts: 19
Location: India
GMAT 1: 610 Q48 V27 GPA: 3.99
WE: Web Development (Computer Software)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)f(a+b)=f(a)∗f(b)?

A. f(x)=x2+1

B. f(x)=52x3

C. f(x)=3x+2f(x)=3x+2

D. f(x)=2x‾‾√f(x)=2x

E. f(x)=24x

f(a+b) should be equal to f(a)*f(b)

Lets take choice E - f(x) = 24^x
F(a+b) = 24^(a+b)
f(a) * f(b) = 24^a * 24^b = 24^(a+b). Similarly we can do this type of expansion for all choices.
Manager  G
Joined: 24 Jun 2013
Posts: 141
Location: India
Schools: ISB '20, GMBA '20
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Substitute x = a+b for F(a+b) in F(x) and x=a for f(a) in f(x) and x=b for f(b) in f(x) and multiply to check both match

E matches

also we can immediately notice that a^x * a^y = a^(x+y) hence E
BSchool Moderator G
Joined: 07 Dec 2018
Posts: 146
Location: India
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

f(a+b)=f(a)∗f(b)

Let's see each option :

1.)
f(x)=$$x^2+1$$

f(a) = $$a^2+1$$
f(b) = $$b^2+1$$
f(a+b)=$$(a+b)^2+1$$
=$$a^2+2ab+b^2+1$$
f(a)*f(b) = $$a^2(b^2+1)+1(b^2+1)$$
= $$a^2b^2+a^2+b^2+1$$

Hence the rule is NOT followed here.
So, the first option is OUT.

2.)
f(x) = $$5^\frac{2x}{3}$$
f(a)=$$5^\frac{2a}{3}$$
f(b)=$$5^\frac{2b}{3}$$
f(a+b) = $$5^\frac{2(a+b)}{3}$$ = f(a)*f(b)

Hence the rule is followed here.

We don't need to check further.

Senior Manager  P
Joined: 18 Jan 2018
Posts: 304
Location: India
Concentration: General Management, Healthcare
Schools: Booth '22, ISB '21, IIMB
GPA: 3.87
WE: Design (Manufacturing)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
f(a+b)=f(a)∗f(b)

this type of function is possible in exponents

A. f(x)=x^2+1
f(a+b) is not equal to f(a)∗f(b)

B. f(x)=5^2x/3
f(a+b) is not equal to f(a)∗f(b)

C. f(x)=3x+2
f(a+b) is not equal to f(a)∗f(b)

D. f(x)=√2x
f(a+b) is not equal to f(a)∗f(b)

E. f(x)= 24^x ===> clearly 24^(a+b) = 24^a * 24^b - Correct
f(a+b) is equal to f(a)∗f(b)
Manager  S
Joined: 09 Apr 2017
Posts: 80
GPA: 3.99
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
for this question, simply plug in a value.
Let's take a=2, b=3

following this equation, f(5) = f(2) * f(3), we evaluate each answer choices.

a. 26 != 50
b. 5^10/3 != 5^10/9
c. 17 != 88
d. sqrt 10 != sqrt 24
e. 24^5 = 24^5

e, wins
Manager  S
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
The question is saying that, if we substitute the value of the function, then both side should we equal.

1. f(x)=x^2+1
f(a+b) = f(a) * f(b)
$$(a+b)^2$$ +1 = ($$a^2$$ +1) * ($$b^2$$ +1)
upon solving we can get that both sides are not equal.

2. $$\frac{(5^{2x})}{(3)}$$
$$\frac{(5^{2(a+b)})}{(3)}$$ = $$\frac{(5^{2a})}{(3)}$$* $$\frac{(5^{2b})}{(3)}$$
Both sides are not equal.

3. 3x+2
3(a+b) +2 = (3a +2) * (3b +2)
Not equal.

4. 2x
$$\sqrt{2(a+b)}$$= $$\sqrt{2a}$$ * $$\sqrt{2b}$$
Not Equal.

5. $$24^x$$
$$24^{a+b}$$ = $$(24^a)$$ * $$(24 ^b)$$
The both side for this equation are equal, as per the indices property.

Please hit kudos if you like the solution. Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 08 Jul 2019, 10:21

Go to page   Previous    1   2   3   4   5    Next  [ 86 posts ]

Display posts from previous: Sort by

# Which of the following function follows the rule: f(a + b) = f(a)*f(b)  