# First note that the larger cube is made up of 1000

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First, note that the larger cube is made up of 1000 smaller cubes. Think about how many cubes are NOT painted. 8 x 8 x 8 inner cubes are not painted which equals 512 cubes. Therefore, 1,000 - 512 = 488 cubes that have some paint. Alternatively, you can calculate this by recognizing that two 10 x 10 sides are painted (200) plus two 10 x 8 sides (160) plus two 8 x 8 sides (128): 200 + 160 + 128 = 488. 8. What is the square root of 7,000,000 (approximately)? You know that 2 * 2 = 4 and that 3 * 3 = 9, and that 1,000 * 1,000 = 1,000,000 so the answer has to be between 2,000 and 3,000. Edge closer in, 2.5 * 2.5 = 6.25 and 2.7 * 2.7 = 7.29 so the answer is approximately 2,600. 9. A closet has three light bulbs inside. Next to the door (outside) are three switches for each light bulb. If you can only enter the closet one time, how do you determine which switch controls which light bulb? Turn on two switches, A and B, and leave them on for a few minutes. Then turn off switch B and enter the room. The bulb that is lit is controlled by switch A. Touch the other two bulbs, which are off. The one that is still warm is controlled by switch B. The third bulb, off and cold, is controlled by switch C. 44 © 2009 Vault.com , Inc. Customized for: Joshua Boylan ( [email protected] ) A.B.FreemanSchool of Business OnlineCareer Library
Vault Guide to Private Equity and Hedge Fund Interviews Brainteasers 10. Four investment bankers need to cross a bridge at night to get to a meeting. They have only one flashlight and 17 minutes left to get to the meeting. The bridge must be crossed with the flashlight and can only support two bankers at a time. The analyst can cross in one minute, the associate can cross in two minutes, the VP can cross in five minutes and the MD takes 10 minutes to cross. How can they all make it to the meeting in time? First, the analyst takes the flashlight and crosses the bridge with the associate. This takes two minutes. The analyst then returns across the bridge with the flashlight, taking one more minute (three minutes passed so far). The analyst gives the flashlight to the VP and the VP and MD cross together, taking 10 minutes (13 minutes passed so far). The VP gives the flashlight to the associate, who re-crosses the bridge taking two minutes (15 minutes passed so far). The analyst and associate now cross the bridge together taking two more minutes. Now, all are across the bridge for the meeting in exactly 17 minutes. 11. A lily in a pond doubles every minute. After an hour, the lily fills the entire pond. When is it one-eighth full? Work backwards. At 59 minutes, it is half full. At 58 minutes, it’s one-fourth full. Thus, after 57 minutes, it is one-eighth full. 12. What is larger, 3^4 or 4^3? 3"4. In most combinations, the lower number " higher number is higher than vice versa because the higher exponential has a powerful multiplier effect. However, 2"3 is higher than 3"2, but you can solve that particular anomaly in your head.