1. 50 cents, 5 cents, (One of the coins is not a nickel, but the other is.)
2. ONE WORD
3. How could a coin have been minted 7 years B.C. (before Christ), when Christ wasn't born yet?
4. I have 1 dime, 1 quarter and 13 nickels.
Solution: Let's say I have n nickels, d dimes and q quarters.
The total number of coins can be represented as n + d + q = 15.
The value of all the coins is 5n + 10d + 25q = 100, since a nickel is worth 5 cents, a dime is worth 10 cents and a quarter is worth 25 cents. Use these two equations to get your answer.
5. He says, "I will be shot." Either that statement is true or false.
If it is true, he Will be hanged. But then being shot wouldn't be true. Thus the statement must be false. But if it is false, he will be shot. But if he is shot, the statement is true. So there is a contradiction; his statement was neither true nor false. They can't shoot him. So they set him free. (Actually, they shot him anyway.)
6.The average rate is greater than the average of the rates. Hint: The average rate is not the same as the average of the rates.
The average rate of a car going uphill at A miles per hour and downhill at B miles per hour the same distance is just 2AB/(A + B). The average of the rates is (A + B)/2. One can show that where A is not equal to B, 2AB/(A + B) is less than (A + B)/2.
7.Terry is 5 years old.
Translate: Alice was 5 years older than Terry is now: a 5 + T (where a is the age that Alice was).Terry is half as old as Alice was: T(½)a . Substitute for a: T (½)(5 + T). We get 2T 5 + T, thus T 5. So Terry is 5 years old.
8. Choice E is correct. An imaginary number is a number that, when multiplied by itself, becomes a negative number. There is no way a real number multiplied by itself will become a negative number. Thus the term "imaginary." Now as an example, 2 times The imaginary number cannot be thought of as greater less than 3 times that number. Thus they are called "not ordered." Real numbers are ordered. For example, 3 times the number 25 is greater than 2 times the number, 25.
9.355 x 356 is greater than 354 x 357 The novice problem-solver will multiply the numbers out - and in 10 seconds, good luck! The experienced problem-solver will realize she doesn't need find the result of the products, just a comparison of them. So she will look for patterns or similarities.
First put the products under columns so you can work with them more easily:
Column A and Column B
354 x 357 and 355 x 356
Divide both columns by 354. Then divide the quantities in the new columns by 356.
Column A and Column B become:
Column A: 357/356 1 and 1/356
Column B: 355/354 1 and 1/354
Column B is therefore greater.
1O. It's better to get a single discount of 50 percent. It is always better to get a single discount of the sums of the successive discounts than the successive discounts. For example, if the item were originally $100, a single discount of 50 percent would give you the item at $50. If you have successive discounts of 20 percent and 30 percent, the first 20 percent discount would give you $80. The second 30 percent discount on $80 would give you $56.
11. How would the lawyer know what the person is dreaming if his client died? That's why his license was revoked. The lawyer should have never wasted the court's time on such a ridiculous matter.
12.THE COLOR IS RED. The third student, who is last to try his luck, reasons, "If I can prove it's impossible that I have a white hat, then I must have a red hat.
There are only three scenarios in which the last student could have a white hat:
(1) if the first student has a red hat and the second student has a white hat. (2) if the first student has a white hat and the second student has a red hat. (3) if the first and second students have red hats.
Scenario (1) is wrong because the first student would know his hat was red if the other two students had white hats, since there were only two white hats in the original bag.
Scenario (2) is wrong because the second student would have made the same deduction.
Scenario (3) is wrong because the second student, would have known she was wearing a red hat if the third student was wearing a white hat. Otherwise the first student would have seen that they were both wearing white hats. But because the second student did not know or figure out that she was wearing a red hat, the third student could not be wearing a white hat.
13. CHOICE C is correct.
Try starting with 4 balls on each side, in the other 4 balls as reference balls if the first set does not balance.
Right Answers, Score
2-4. Above average
5-6. Very smart
7-8. Very, very smart to near genius
9-1 0. Genius
13. Super genius
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