12 Days of Christmas GMAT Competition - Day 6: If n = (23.57111317

Question

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

If  n = (23.57111317 * 10^5)^{11} , how many digits are to the right of the decimal point of n?

A. 3
B. 8
C. 30
D. 33
E. 55

Bunuel · Accepted Answer

GMAT Club's Official Explanation:

(23.57111317 * 10^5)^{11} =

= (2357111317 * 10^{-8} * 10^5)^{11} =

= (2357111317 * 10^{-3})^{11} =

= 2357111317^{11} * 10^{-33}

Whatever the value of  2357111317^{11}  is,  10^{-33}  will shift the decimal point of that number 33 places to the left.

Answer: D.

siddhantvarma · Answer

n = (23.57111317×10^5)^11

Move decimal in base:
 23.57111317× 10^5  = 2357111.317

When raising a decimal to a power, multiply decimal places by power:
 Base has 3 decimal places
 Power is 11
 3 × 11 = 33 decimal places

Therefore n has 33 digits after the decimal point.

Answer: D. 33

Kinshook · Answer

If  n = (23.57111317 * 10^5)^{11} , how many digits are to the right of the decimal point of n?

23.57111317 * 10^5 = 2357111.317 = 2357111317*10{-3} 
 n = (2357111317*10^{-3})^{11} = (2357111317)^{11} *10^{-33}

The number of digits to the right of decimal points of n = 33

IMO D

HarshaBujji · Answer

This number n can also be represented as below .

(2357111317 * 10^-3)^11  =>  Some large number * 10^-33.

So it is obvious that there are 33 digits after decimal. 
 
IMO D

AbhiS101 · Answer

The base 23.5711131723.5711131723.57111317 has  8 digits  after the decimal point.
When raised to the 11-th power, the digits after the decimal become: 8×11=88 
Multiplication by 10^55 shifts the decimal point  55 places to the right ,
 leaving: 88−55=3388 - 55 = 3388−55=33

IMO D

Heix · Answer

If n=(23.57111317∗105)11
n
=
(
23.57111317
∗
10
5
)
11
, how many digits are to the right of the decimal point of n?

A. 3
B. 8
C. 30
D. 33
E. 55

Show Spoiler

Attachment:

GMAT-Club-Forum-durfgvrn.jpeg [ 177.87 KiB | Viewed 1371 times ]

Krunaal · Answer

n can be simplified and written as  (2357111.317)^11

Number of digits after decimal point (d) = 3
n is raised to the power (p) = 11

When a number with d decimal digits is raised to a power p, the total number of decimal digits become: d*p
=> 3*11 =  33

Answer D.

A_Nishith · Answer

Step 1:  Rewrite the expression
We can express n as:

n=(23.57111317)^11 * 8(10^5)^11
 =(23.57111317)^11 * 10^55
 
 Step 2:  Analyze

(23.57111317)^11
 
The number 
23.57111317 has 8 digits to the right of the decimal point. When a decimal number is raised to a power p, the number of digits to the right of the decimal point in the result is

p⋅(number of digits to the right of the decimal point in the base).

Here, 
p=11, and the base has 8 digits to the right of the decimal point. Therefore:

Number of digits to the right of the decimal point in (23.57111317)^11
 =11*8=88.

Step 3:  Effect of 10^55
The multiplication by 10^55 shifts the decimal point 55 places to the right. This reduces the number of digits to the right of the decimal point in 
(23.57111317)^11

Thus:
Remaining digits to the right of the decimal point=88−55=33

Final Answer: 33 
​

hr1212 · Answer

n = (23.57111317 * 10^5)^{11}

n = (2357111317 * 10^{-8} * 10^5)^{11}

n = (2357111317 * 10^{-3})^{11}

n = (2357111317)^{11} * (10^{-3})^{11}

n = (2357111317)^{11} * (10)^{-33}

Hence, no of decimal points are 33.

Answer: D

nishantswaft · Answer

To determine how many digits are to the right of the decimal point in n= (23.57111317× 10^5 )^11, let's break it down step by step.

We can rewrite nnn as:
n= (23.57111317)^{11} ×( 10^5 )^11 
n= (23.57111317)^{11} × 10^{55}

The number 23.57111317 has 8 digits to the right of the decimal point. When raised to the power of 11, the number of decimal places increases proportionally:

Decimal places in  (23.57111317)^{11}  =8×11=88

Multiplying  (23.57111317)^{11}  by  10^{55}  shifts the decimal point 55 places to the right.
Therefore:
Net decimal places in n=88−55=33

Answer is D

AVMachine · Answer

n=(23.57111317∗105)^11; This can be simplified as: (2357111.317)^11;

Now I didn't know further so I took some examples. .7*.7 = .49
.4*.4=.16; .5*.5=.25; 1.6*1.6= 2.56

Hence, the final answer will have 3*11=33 decimals in it.

crimson_king · Answer

For solving this particular question, we split the numbers into two parts-

23.57111317^11 & (10^5)^11

Considering just 23.57111317 there are 8 digits to the right of the decimal point & on raising this number to the power of 11, there will be 8*11=88 digits to the right of the decimal point.

On multiplying this number with (10^5)^11=10^55 the decimal shifts 55 places to the right. In this situation the number of digits to the right of the decimal point of n would ideally be-

88-55=33 digits

Hence the answer to this question is option (D) 33

Eswar69 · Answer

23.57111317 - This number contains 8 digits after the decimal point.
10^5 = 2357111.317 - This number contains 3 digits after the decimal point.

2 methods of solving it.

Method 1 
(2357111.317)^11 which means 3 digits after the decimal points
3 * 11 = 33

Method 2 
(23.57111317)^11 = 8 * 11 = 88 digits after the decimal points
(10^5)^11 = 10^55 = 55 digits
88-55 = 33

is the correct answer.

Karanjotsingh · Answer

Start with the Number: 
 
 23.57111317 has  8 digits  after the decimal point.  
 
  Raise to the 11th Power: 
 
 When you raise a number with 8 decimal places to the 11th power, the total decimal digits become 8×11=88.  
 
  Multiply by 10^55: 
 
 Multiplying by 10^55 moves the decimal point  55 places to the right . 
 This reduces the number of decimal digits: 88−55=33.  
  
 Conclusion: 
There are  33 digits  to the right of the decimal point in n.

Answer: 
 D. 33

Mardee · Answer

n=(23.57111317∗10^5)^11

Now,
23.57111317∗10^5 = 2357111.317

=> n = (2357111.317)^11

Number of digits to the right of the decimal point = 3 x 11 (no of digits right of decimal point x power)
 =  33

D. 33

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12 Days of Christmas GMAT Competition - Day 6: If n = (23.57111317

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