1.
https://gmatclub.com/forum/mary-needs-3 ... 29298.htmlMary needs 30 liters of a mocktail consisting of cranberry, apple, and grape juice for a party. Each juice must constitute at least 20% and at most 80% of the mocktail.
In the table, select for
Maximum the greatest possible quantity of any juice in liters in the mocktail, and select for
Minimum the least possible quantity of any juice in liters in the mocktail. Make only two selections, one in each column.
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Given that each juice must constitute at least 20% and no more than 80% of the mocktail, each juice must be at least 0.2 * 30 = 6 liters and at most 0.8 * 30 = 24 liters in the mocktail.
To maximize the quantity of one specific juice, we should minimize the quantities of the remaining two juices. Since the minimum quantity for any juice is 6 liters, the combined minimum for two juices is 6 + 6 = 12 liters. This makes the maximum possible quantity of the third juice equal to 30 - 12 = 18 liters.
As for the minimum quantity, it would simply be the minimum set by the recipe, which is 6 liters.
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2.
https://gmatclub.com/forum/a-palindrome ... 30148.htmlA palindrome is a number that reads the same forward and backward. For example, 13231 and 111 are palindromes.
Select for
Even Palindromes the number of 6-digit numbers that are palindromes composed of even digits and select for
Odd Palindromes the number of 6-digit numbers that are palindromes composed of odd digits.
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A 6-digit number to be a palindrome must be in the form of xyzyx. Note that one or more digits of a palindrome can be the same, thus two or all three from x, y, and z can be the same digit.
For a 6-digit number to be a palindrome composed of even digits, each of y and z can take all five even digit values: 0, 2, 4, 6, and 8. However, x can only take four values: 2, 4, 6, and 8, because a 6-digit number cannot start with 0. That would make the number a five-digit number instead. Therefore, the number of 6-digit numbers that are palindromes composed of even digits is 4*5*5 = 100.
For a 6-digit number to be a palindrome composed of odd digits, each of x, y, and z can take all five odd digit values: 1, 3, 5, 7, and 9. Therefore, the number of 6-digit numbers that are palindromes composed of odd digits is 5*5*5 = 125.