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

 It is currently 09 Dec 2019, 00:53 ### 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  S
Joined: 27 Mar 2018
Posts: 79
Location: India
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
A. a^2+b^2+2ab+1 != a^2+b^2+2

B. 5^2(a+b)/3 != 5^2a/3 *5^2b/3 => 5^2(a+b)/9

C. 3(a+b)+2 != 3(a+b)+4

D. $$\sqrt{2(a+b)}$$ != 2ab

E. 24^(a+b) = 24^a * 24^b => 24^(a+b)

Manager  S
Joined: 10 Aug 2016
Posts: 68
Location: India
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)

A. f(x)=x^2+1
f(a+b) = (a+b)^2 + 1
f(a)*f(b) = (a^2 + 1)*(b^2 + 1)
clearly not equal. incorrect.

B. f(x)=(5^2x)/3
f(a+b) = (5^2(a+b))/3
f(a)*f(b) = (5^2a)/3 * (5^2b)/3 = (5^2(a+b))/9
Not equal. Incorrect.

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

D. f(x)=sqrt(2x)
f(a+b) = sqrt(2(a+b))
f(a)*f(b) = sqrt(2a)*sqrt(2b) = 2*sqrt(ab)
Not equal. Incorrect

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

Intern  B
Joined: 06 Jul 2018
Posts: 31
Location: India
Schools: ISB '21
GMAT 1: 670 Q49 V33 Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Correct Answer is E i.e. 24^x
Question is f(a+b) = f(a).f(b) example 2+2 = 2*2
Now plug in 4 in each function and plug in 2 in each function and square the result
Which ever option gives same answer is correct
Manager  G
Joined: 06 Feb 2019
Posts: 110
Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Let a = 2 and b=3

24^5=24^2 * 24^3

Posted from my mobile device
Manager  G
Joined: 19 Apr 2017
Posts: 168
Concentration: General Management, Sustainability
Schools: ESSEC '22
GPA: 3.9
WE: Operations (Hospitality and Tourism)
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)

30 seconds approach
If you look at the answers and notice the Product Rule. it cut shorts the time
The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents.

2 min approach:Solving using number picking
lets assume a=2,b=2, a+b=4

f(a+b)=(4)^2+1 = 17
f(a)∗f(b)=(2^2+1)(2^2+1)=25 False

f(a+b)=[(5)^2*4]/3 = [5^8]/3
f(a)∗f(b)=[5^2*2]/3*[5^2*2]/3 False

f(a+b)=(4)+2 = 6
f(a)∗f(b)=(3(2)+2)(3(2)+2)=8*8 False

f(a+b)=√2*4=√8
f(a)∗f(b)=(√2*2)(√2*2)=√16 False

f(a+b)=$$24^4$$
f(a)∗f(b)=$$(24^2)*(24^2)=24^4$$ TRUE

Manager  S
Joined: 06 Aug 2018
Posts: 97
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1

The fight was between A and E

E is true in all.conditions

A fails at a=-1 and b=1

So hence answer is definitely E

Posted from my mobile device
Director  P
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
It is obvious only option E will satisfy. Still the workings

A. f(x)=x^2+1 ; f(a+b) = (a+b)^2+1 and f(a)*f(b) = a^2*b^2 + a^2 + b^2 +1 - Not Equal

B. f(x)=5^2x/3 ; f(a+b) = 5^2(a+b)/3 and f(a)*f(b) = 5^2(a)/3*5^(b)/3 - Not Equal as denominator will be 9

C. f(x)=3x+2 ; f(a+b) = 3(a+b)+2 and f(a)*f(b) = 3(a+2)*3(b+2) - Not Equal

D. f(x)=√2x ; f(a+b) = √2(a+b) and f(a)*f(b) = 2√ab - Not Equal

E. f(x)=24^x ; f(a+b) = 24^(a+b) and f(a)*f(b) = 24^a*24^b=24^(a+b) - Equal

IMO E
Manager  G
Joined: 18 Jun 2013
Posts: 139
Location: India
Concentration: Technology, General Management
GMAT 1: 690 Q50 V35 GPA: 3.2
WE: Information Technology (Consulting)
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)?

Method 1: As per the rule that needs to be true, we can foresee that if the variable is in exponentials then a mere multiplication can simply lead to addition and the rule can hold true for the equation.

As per this, we see that the options 2 and 5 are the only ones where the variable is completely in the exponentials.

In option 2 the denominator will not allow the rule to hold true as in the RHS it will multiply. Hence option 2 is not correct.

In option 5, we have no other issues and the variable in the exponentials will simply add up on multiplication of the entities and hence the rule will always hold true.

Now, we can plug in some sample values and see if our analysis is correct and mark the correct answer which is option E.

Method 2: Putting values. This method is fool proof but may take you a couple of minutes to solve this question.

Option 1: f(x)=x^2+1

f(1 + 1) = f(1) = 1^2 + 1 = 5
f(1) = 1^2 + 1 = 2

If rule is true here then,
f(1 + 1) = f(1) * f(1)

However,
5 <> 2

Hence,
f(1 + 1) <> f(1) * f(1)

Option 1 is not correct.

Option 2: f(x) = (5^(2x))/3

f(1 + 1) = f(2) = (5^(2*2)) / 3 = (5^4) / 3 = 625/3
f(1) = (5^(2*1)) / 3 = 25/3

If rule is true here then,
f(1 + 1) = f(1) * f(1)

625/3 = 25/3 * 25/3 -> Rule holds here.

f(1 + 0) = f(1) = (5^(2*1)) / 3 = 25/3
f(1) = (5^(2*1)) / 3 = 25/3
f(0) = (5^(2*0)) / 3 = 1/3

However,
25/3 <> 25/3 * 1/3

Now,
f(1 + 1) = f(1) * f(1);
BUT, f(1 + 0) <> f(1) * f(0);

Hence, rule holds true sometimes but not always for this option.

Option 2 is not correct.

Option 3: f(x) = 3x + 2

f(1 + 1) = f(2) = 3*2 + 2 = 8
f(1) = 3*1 + 2 = 5

If rule is true here then,
f(1 + 1) = f(1) * f(1)

However,
8 <> 5 * 5

Hence,
f(1 + 1) <> f(1) * f(1)

Option 3 is not correct.

Option 4: f(x) = sqrt(2*x)

Consider,
f(1 + 1) = f(2) = sqrt(2*2) = 2
f(1) = sqrt(2*1) = sqrt(2)

If rule is true here then,
f(1 + 1) = f(1) * f(1)

And,
2 = sqrt(2) * sqrt(2)

Now consider,
f(2 + 3) = f(5) = sqrt(2*5) = sqrt(10)
f(2) = sqrt(2*2) = 2
f(3) = sqrt(2*3) = sqrt(6)

However,
sqrt(10) <> 2 * sqrt(6)

Hence,
f(1 + 1) <> f(1) * f(1)

Option 4 is not correct.

Option 5: f(x) = 24^x

Consider,
f(1 + 1) = f(2) = 24^2
f(1) = 24^1

If rule is true here then,
f(1 + 1) = f(1) * f(1)

And,
24^2 = 24^1 * 24^1

Consider,
f(2 + 3) = f(5) = 24^5
f(2) = 24^2
f(3) = 24^3

If rule is true here then,
f(1 + 1) = f(1) * f(1)

And,
24^5 = 24^2 * 24^3

Hence Option 5 or Option E is correct.
Senior Manager  P
Joined: 27 Aug 2014
Posts: 368
Location: Netherlands
Concentration: Finance, Strategy
Schools: LBS '22, ISB '21
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1

substituting a+b once for x in E yields
24^(a+b)
f(a)*f(b) = 24^aX24^b = 24^(a+b)

rest all equations yield different results. so E
Manager  G
Joined: 29 Nov 2018
Posts: 168
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
let a=1
b=2

E. f(a+b) = f(3)= 24^3
f (a) = 24
f (b) = 24^2
f (a) * f(b) = 24^3

IMO option E
Director  P
Joined: 18 May 2019
Posts: 530
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)
We know that x^(a+b)={x^a}*{x^b}. The function in the answer choices that most resemble this property is E. So I will test for this option first.
f(x)=24^x. f(a)=24^a and f(b)=24^b.
f(a+b)=24^(a+b)
f(a)*f(b)=(24^a)*(24^b) =24^(a+b).

Posted from my mobile device
Director  V
Status: Manager
Joined: 27 Oct 2018
Posts: 748
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
for $$f(x)=x^2+1$$:
f(a+b) = $$(a+b)^2 + 1 = a^2 + b^2 + 2ab + 1$$
f(a)∗f(b) = $$a^2 + 1 + b^2 + 1 = a^2 + b^2 + 2$$ --> not equal for all values

for $$f(x)=\frac{5^{2x}}{3}$$:
f(a+b) = $$\frac{5^{2(a+b)}}{3} = \frac{5^{2a}5^{2b}}{3}$$
f(a)∗f(b) = $$\frac{5^{2a}}{3}*\frac{5^{2b}}{3} = \frac{5^{2a}5^{2b}}{9}$$--> not equal for all values

for $$f(x)=3x+2$$:
f(a+b) = $$3(a+b) + 2 = 3a + 3b + 2$$
f(a)∗f(b) = $$(3a+2)(3b+2) = 9ab + 6b + 6a + 4$$ --> not equal for all values

for f(x)= $$\sqrt{{2x}}$$:
f(a+b) = $$\sqrt{{2(a+b)}} = \sqrt{{2a+2b}}$$
f(a)∗f(b) = $$\sqrt{{2a}}* \sqrt{{2b}} = \sqrt{{4ab}} = 2\sqrt{{ab}}$$ --> not equal for all values

for $$f(x)= 24^x$$:
f(a+b) = $$24^{a+b}$$
f(a)∗f(b) = $$24^{a}*24^{b} = 24^{a+b}$$ --> equal

E
Manager  P
Joined: 01 Aug 2017
Posts: 220
Location: India
GMAT 1: 500 Q47 V15 GPA: 3.4
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
Which of the following function follows the rule: f(a+b)=f(a)∗f(b)?

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

B. f(x)=$$5^2^x * 3$$

C. f(x)=3x+2

D. f(x)=$$\sqrt{2x}$$

E. f(x)=$$24^x$$

A - f(a) = $$a^2 +1$$ f(b) = $$b^2 +1$$ f(a+b) = $$(a+b)^2 +1$$.
f(a) * f(b) = $$a^2*b^2 +a^2+b^21$$
Clearly f(a+b) is not equal to f(a)∗f(b).

B - f(a)=$$5^2^a * 3$$ f(b)=$$5^2^b * 3$$ f(a+b)=$$5^2^(a+b) * 3$$.
f(a) * f(b) = $$5^2^a+b * 9$$
Clearly f(a+b) is not equal to f(a)∗f(b).

C - f(a)=$$3a+2$$ f(b)=$$3b+2$$ f(a+b)=$$3(a+b)+2$$.
f(a) * f(b) = $$9ab+6a+6b+4$$
Clearly f(a+b) is not equal to f(a)∗f(b).

D - f(a)=$$\sqrt{2a}$$
f(b)=$$\sqrt{2b}$$
f(a+b)=$$\sqrt{2(a+b)}$$
f(a)*f(b)=$$\sqrt{4ab}$$
Clearly f(a+b) is not equal to f(a)∗f(b).

E - f(x)=$$24^x$$

f(a)=$$24^a$$
f(b)=$$24^b$$
f(a+b)=$$24^(a+b)$$
f(a) * f(b)=$$24^(a+b)$$.
Clearly f(a+b) is equal to f(a)∗f(b)

Hence E
Senior Manager  P
Joined: 13 Feb 2018
Posts: 480
GMAT 1: 640 Q48 V28 Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
GMAT likes to throw such questions to waste your precious time.
Per my experience, the first two options are definitely the wrong answer you have to sweat searching for correct option Let's begin

A) $$(a^2+1)*(b^2+1)=(a+b)^2+1$$; at a glance on the left side, we will have $$a^2*b^2$$ that is impossible for the right hand. NO
B) $$5^{2a+2b}/9=5^{2a+2b}/3$$; NO
C) $$(3a+2)*(3b+2)=3(a+b)+2$$; NO
D) $$\sqrt{4ab}=\sqrt{2a+2b}$$ NO
Last one hold the breath, otherwise you have to go back checking all the options once again
E) $$24^a*24^b=24^{a+b}$$

IMO
Ans: E
Manager  S
Joined: 21 Jan 2019
Posts: 100
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
Quote:
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+1f(x)=x2+1

B. f(x)=52x3f(x)=52x3

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

D. f(x)=2x‾‾√f(x)=2x

E. f(x)=24x

Here among all the options only in option e,

f(a+b) = f(a) * f(b)
as exponents add each other when multiplied.
base wont matter here.
Option E.
Manager  G
Joined: 29 May 2019
Posts: 122
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)?

We have to look for the option in which addition and multiplication might result in same value.
If we look at the answer choices we can eliminate A, C and D easily. But to make sure we will put value of x and check.

A. f(x)=x^2+1
f(a+b)= (a+b)^2+1
f(a)*f(b) = (a^2 + 1)* (b^2+1)
after solving we do not get similar values.

B. f(x)=5^2x/3
f(a+b)=5^2(a+b)/3
f(a)*f(b)=5^2a/3* 5^2b/3
After solving this we get same numerator but different denominator.

C. f(x)=3x+2
f(a+b)=3(a+b)+2
f(a)*f(b)=(3a+2)*(3b+2)
after solving we do not get similar values.

D. f(x)=sq root of 2x
f(a+b)=sq root of 2(a+b)
f(a)*f(b)=sq root of 2a * sq root of 2b
after solving we do not get similar values.

E. f(x)=24^x
f(a+b)=24^(a+b)
f(a)*f(b)=24^a* 24^b
We get similar values on both sides.
Correct.

_________________
Pick yourself up, dust yourself off, and start again.

Success is the sum of all small efforts.

MAKE IT HAPPEN Senior Manager  P
Joined: 20 Mar 2018
Posts: 407
Location: Ghana
Concentration: Finance, Real Estate
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)
So too many variables here let’s solidify it.
let a= -1 , b=1
.: f(-1+1) = f(-1)•f(1) —>
f(0)= f(-1)•f(1)

(a) f(x) = x^2+1
f(0)= 0^2+1 =1 and f(-1)•f(1)=
f(-1^2+1)•f(1^2+1) =4
So 1 is not equal to 2 (doesn’t follow rule)

(b) f(x)=((5)^2x)/3
f(0)=5^0/3 =1/3 and
f(-1)•f(1)=f(5^(-2)/3)•f(5^2/3)
= (1/3•25)•(25/3) =1/9
1/3 not equal to 1/9

(c) f(x) = 3x+2
f(0)=3(0)+2 =2 and f(-1)•f(1)= f(3(-1)+2)•f(3(1)+2)= -5

(d) f(x) = (sqrt.2x)
f(0)=( sqrt.2(0))= 0 and
f(-1)•f(1)= f(sqrt.2(-1))•f(sqrt2(1)) =2i

(e) f(x) = 24^x
f(0) = 24^0 = 1 and f(-1)•f(1)= f(24^-1)•f(24)= 1
1 equals 1 follows rule of f(0) = f(-1)•f(1)

Posted from my mobile device
Senior Manager  G
Joined: 12 Sep 2017
Posts: 308
Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
$$24^x$$ where a = 2, b= 2.

$$f(a + b) = f(a) * f(b)$$

$$f(2 + 2) = f(2) * f(2)$$

$$4 = 4$$

For $$f(a + b)$$

$$24^4 = (3^4 * 2^12)$$

For $$f(a) * f(b)$$

$$24^2 * 24^2$$

$$(2^6 * 3^2) * (2^6 * 3^2)$$

$$(2^12 * 3^4)$$

E
Manager  G
Joined: 28 Jan 2019
Posts: 127
Location: Peru
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, if we replace, we have (a+b)^2 +1 ≠ (a^2+1)*(b^2 +1)

B. f(x)=5^2x/3, if we replace, we have 5^2(a+b)/3 ≠ (5^2a/3)*(5^2b/3)

C. f(x)=3x+2, if we replace, we have 3(a+b)+2 ≠ (3(a+2))*(3(b+2))

D. f(x)=√2x, if we replace, we have √2(a+b) ≠ √2a*√2b

E. f(x)=24x, if we replace, we have 24^(a+b) = 24^a*24^b

Intern  S
Joined: 08 Jun 2019
Posts: 29
Location: India
GPA: 3.8
Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)  [#permalink]

### Show Tags

1
IMO - E

Because 24^x

for f(a+b) = 24^(a+b) = 24^a*24^b
for f(a)*f(b) = 24^a*24^b.
_________________
580 | 560 | Hoping For the best Re: Which of the following function follows the rule: f(a + b) = f(a)*f(b)   [#permalink] 08 Jul 2019, 20:01

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)  