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does that work better?
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👍👍 good luck!
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Permutation and combination question :

a 10 digit number, which can include any number from 0 to 9. the first digit shall only be 6,7,8,9 and in the whole 10 digit number no digit should be repeated more than 4 times. like it's upto 4 repetitions of any number are allowed. how many such possible 10 digit numbers exist?
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4*10*10*10*9*9*9*9*8*8 ??
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sigmabale
Permutation and combination question : a 10 digit number, which can include any number from 0 to 9. the first digit shall only be 6,7,8,9 and in the whole 10 digit number no digit should be repeated more than 4 times. like it’s upto 4 repetitions of any number are allowed. how many such possible 10 digit numbers exist?
This looks like a nasty casework :(
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What’s the answer?
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Data Sufficiency Butler: April 2024
April 18DS 1DS 2
­
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Problem Solving Butler: April 2023
April 18PS 1PS 2
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Data Sufficiency Butler: April 2024
April 19DS 1DS 2
­
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April 19PS 1PS 2
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Hi

Lemonade A has a lemon acid to water ratio of 1:4, and Lemonade B has a lemon acid to water ratio of 1:5. In a mixture combining the two lemonades, the lemon acid to water ratio is 9:41. What is the ratio of the amount of Lemonade A to the amount of Lemonade B in this combined mixture?

Is there a shortcut to solve this question ?
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michmello271998
Hi

Lemonade A has a lemon acid to water ratio of 1:4, and Lemonade B has a lemon acid to water ratio of 1:5. In a mixture combining the two lemonades, the lemon acid to water ratio is 9:41. What is the ratio of the amount of Lemonade A to the amount of Lemonade B in this combined mixture?

Is there a shortcut to solve this question ?
­This question is discussed here:

https://gmatclub.com/forum/m07-183762.html

Hope this helps.

P.S. Not all questions have a shortcut solutions. 
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@Bunuel i add some comment in question
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Is there a shortcut to solve this question ?
use allegations its there in comment section of link
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Please help with this
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What is problem? Calculate a and b?
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anyone can solve the problem on the circle
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