超强GMAT备考资料-Difficult Problems from the Math Section gmat problems.docVIP

Difficult Problems from the Math Section The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=? Sol: First term a=2, common difference d=2 since even numbertherefore sum to first n numbers of Arithmetic progression would ben/2(2a+(n-1)d)= n/2(2*2+(n-1)*2)=n(n+1) and this is equal to 79*80therefore n=79 which is odd... The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?(A) $4.50(B) $5.10(C) $5.30(D) $5.50(E) $5.60 Soln: 320 + 5x = 580 - .41x; x = # of days after price is same; solving for x; x is approximately 48, thus the required price is 320 + 5 * 48 = 560 cents = $5.6 How many randomly assembled people do u need to have a better than 50% prob. that at least 1 of them was born in a leap year? Soln: Prob. of a randomly selected person to have NOT been born in a leap yr = 3/4Take 2 people, probability that none of them was born in a leap = 3/4*3/4 = 9/16. The probability at least one born in leap = 1- 9/16 = 7/16 0.5Take 3 people, probability that none born in leap year = 3/4*3/4*3/4 = 27/64. The probability that at least one born = 1 - 27/64 = 37/64 0.5Thus min 3 people are needed. In a basketball contest, players must make 10 free throws. Assuming a player has 90% chance of making each of his shots, how likely is it that he will make all of his first 10 shots? Ans: The probability of making all of his first 10 shots is given by(9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10) = (9/10)^10 = 0.348 = 35% AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?(