GMAT Reasoning questions(Like Games) Flashcards
Rita and Sam play the following game with n sticks on a table. Each must remove 1, 2, 3, 4 or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?
https://gmatclub.com/forum/rita-and-sam-play-the-following-game-with-n-sticks-on-a-table-each-mu-130173.html
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 ?
You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4, and 5 then no two numbers out of these 6 add up to 10.
Now, the next, 7th number whatever it’ll be (6, 7, 8, or 9) will guarantee that two number WILL add up to 10. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10.
ANS = 7
Let n and k be positive integers with k ≤ n. From an n × n array of dots, a k × k array of dots is selected. The figure above shows two examples where the selected k × k array is enclosed in a square. How many pairs (n, k) are possible so that exactly 48 of the dots in the n × n array are NOT in the selected k × k array?
A. 1 B. 2 C. 3 D. 4 E. 5
In general, an n x n array will have a total of n² dots
Likewise, an k x k array will have a total of k² dots
So, n² - k² = the number of dots in the n × n array that are NOT in the k × k array
If there are 48 dots in the n × n array but NOT in the k × k array, we can write: n² - k² = 48
so product of n-k and n+k has to be 48 and since the product is even, at least one of n-k or n+k should be even.
But n-k and n+k will have the same property, so both have to be even…
check for even numbers whose product is 48..
(a) 48=224
so n-k=2 and n+k=24..Add both, so 2n=26..n=13 and k=11
(b) 48=412
so n-k=4 and n+k=12..Add both, so 2n=16..n=8 and k=4
(c) 48=6*8
so n-k=6 and n+k=8..Add both, so 2n=14..n=7 and k=1
3 cases
https://gmatclub.com/forum/the-shaded-region-in-the-figure-above-represents-a-rectangular-frame-135095.html
A circle is drawn within the interior of a rectangle. Does the circle occupy more than one-half of the rectangle’s area?
(1) The rectangle’s length is more than twice its width.
(2) If the rectangle’s length and width were each reduced by 25% and the circle unchanged, the circle would still fit into the interior of the new rectangle.
ans = d
