12 Days of Christmas GMAT Competition - Day 6: If n = (23.57111317 : Problem Solving (PS)

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23 Dec 2024, 19:31

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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

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23 Dec 2024, 21:05

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The no. of digits after decimal depend upon the no. of times a no. is div. by 10.

so,
n= (23.57111317*10^5)^11
=> (2357111317 * 10^-8 * 10^5)^11
=>2357111317 * 10^-88 * 10^55
=> 2357111317 * 10^-33.

So, after decimal there will be 33 digits.

Ans- 33

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23 Dec 2024, 22:01

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n = (2357111.317)^11
Since 371 are the last 3 digits / right of decimal point, the number of digits at the right would be -
Number of digits to the right * power
3 * 11 = 33

IMO D

Bunuel

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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

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

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23 Dec 2024, 22:36

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n = (2357111.317)^11.

Total digits = 3 x 11 = 33.

Answer: D

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23 Dec 2024, 22:59

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I would say answer D

(23.57111317∗10^5) = 2357111.317
(23.57111317∗10^5)^11 = 2357111.317^11
We have 3 digits to the right of the of the decimal point power 11
11x3 = 33 -> answer D

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23 Dec 2024, 23:11

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Hi All,

Simplifying the equation

we get n= $(2357111.317)[color=#000000]^11;$,[/color]

so to find out the no of digits after the no is muplitplied to the power, we can take examples of smaller numbers and how they are behaving,

eg $(0.5)[color=#000000]^2;$ will give 0.25, there fore get observe that if $10^1;$ is denomenator, leads to $10^2;$. [/color]

eg 2 , $(2.1)[color=#000000]^3;$ will give 9.261 [/color]

from both the examples we can deduce that the no of digits after decimals= no of digit before the power x the power its raised to

therefore from n we get = 3 x 11

That is 33 , therefore the answer

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23 Dec 2024, 23:22

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Bunuel

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

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

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

[D] is the correct answer.

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23 Dec 2024, 23:40

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(3 decimals )^11
This there are 33 digits after decimal
(10^-3)^11

And d

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24 Dec 2024, 00:02

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Answer is D. 33

The digits to the right of the decimal point = n * existing digits after decimal

23.57111317 * 10^5 = 2357111.317. We take 11 * 3 existing digits = 33 for the answer

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24 Dec 2024, 00:31

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First need to solve inside the bracket

so, it will become (2357111.317)^11

The general rule is multiplication of number of digits after decimal point with the exponent

Hence, $n=3*11= 33$

IMO D

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24 Dec 2024, 02:31

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We need to find how many digits are to the right of the decimal point in n = (23.57111317 × 10^5)^11.

--> The number 23.57111317 has 8 decimal places. Multiplying it by 10^5 shifts the decimal 5 places to the right, leaving 3 decimal places.

--> Raising it to the power of 11 multiplies the decimal places by 11. So, 3 × 11 = 33.

Final Answer: 33 digits. Option D.

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24 Dec 2024, 04:39

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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

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24 Dec 2024, 05:08

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n = (23.57111317* 10^5 )^11
remove the decimal and convert the value in the bracket to int (without decimal and power of 10s)
so n = integer * [10 power -3] power 11
expanding given us n = int * 10 power -33
so 33 digits

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24 Dec 2024, 05:46

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

In 2357111317^11 there are no trailing zeros (its last digit is 3) and, since it is divided by 10^(-33), the number of digits to the right of the decimal point of n is 33.

Answer D

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24 Dec 2024, 05:59

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The correct answer is D.

Because 5 squared of 10 removes 5 digits of 23.57111317. That will be 2357111.317
Now we can calculate that 3*11=33.

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24 Dec 2024, 06:07

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Quote:

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

Simplify = (2357111.317)^11
Ignore 2357111, focus on (0.317)^11 = 3 digits * 11 = 33 digits -> there should be 33 digits to the right of decimal point

Choose D

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24 Dec 2024, 06:25

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IMO D

n=(23.57111317∗10^5)^11

Now new number is

n=(2357111.317)^11

Now taking the point after decimal

0.317 ^ 11

for ex if the number would have been

.5 ^2 then point afgter decimal would be 2

if it would be

0.3^4 then point after decimal would be 4

Using analogy

0.317 ^ 11

points after decimals is 11*3 = 33

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