The GMAT is a tricky test, so make sure you can solve the easy problems. Test yourself with the following problems. Questions1. The value of an investment triples every 10 years. By what factor does the value increase over a 30year period? (A) 3 (B) 6 (C) 9 (D) 27 (E) 30 2. A chemist is making a 50% alcohol solution. How many milliliters of distilled water must the chemist add to 600 milliliters of an 80% alcohol solution to obtain a 50% solution? (A) 180 (B) 300 (C) 360 (D) 480 (E) 600 3. An investor receives interest on two simple interest investments, one at 3%, annually, and the other at 2%, annually. The two investments together earn $900 annually. The amount invested at 3% is $20,000. How much money is invested at 2%? (A) $10,000 (B) $12,000 (C) $15,000 (D) $20,000 (E) $35,000 4. If the diameter of a circle is 14, then the area of the circle is (A) 7pi (B) 14pi (C) 28pi (D) 49pi (E) 196pi Answers1. (D) Make it easy by keeping it simple. Let the investment be $100. In 10 years, it will triple to $300. In another 10 years, which is 20 years, it will triple to $900, and then in 30 years, it will triple from $900 to $2,700. Since 2,700 is 27 times 100, the investment increase by a factor of 27. 2. (C) Let x = number of milliliters of distilled water to be added. So we have, 0%.x + 80% (600) = 50% (x + 600) or, 0.8 (600) = 0.5 ( x + 600) or, 480 = 0.5x + 300 or, 0.5x = 180 or, x = 360. The chemist must add 360 milliliters of distilled water. 3. C. The simple interest formula is I = PRT. Let x be the amount invested at 2% annually, so you can set the equation as: 2%x + 3%($20,000) = $900 or, 0.02x + 0.03($20,000) = $900 or, 0.02x + $600 = $900 or, 0.02x = $300 or, x = $300/0.02 = $15,000 $15,000 is invested at 2%. 4. D
The diameter is twice the radius, so the radius is 7. The area of the circle is pi.r^2 = pi.7^2 = 49pi. So the area of the circle is 49pi.
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