A positive integer, x, is divisible by 15, 25, and 30. Which of the following is the smallest possible value of x?
a) 75 b) 90 c) 120 d) 150 e) 450 From an old ACT Exam. SOLUTION The answer is choice d. The smallest number that is divisible by 15, 25, and 30 is the Least Common Multiple (LCM) of all the numbers. First factor all the given numbers. 15 = 3 * 5 25 = 5 * 5 30 = 2 * 3 * 5 Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs. 2: 1 occurrence 3: 1 occurrence 5: 2 occurrences LCM = 2 * 3 * 5 * 5 = 150 Therefore, the answer is choice d) 150.
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There are 25 buildings on Maple Street. Of these 25 buildings, 10 have fewer than 6 rooms, 10 have more than 7 rooms, and 4 have more than 8 rooms. What is the total number of buildings on Maple street that have 6,7, or 8 rooms?
a) 5 b) 9 c) 11 d) 14 e) 15 SOLUTION: The answer is choice c. GIVEN: There are 25 buildings. 10 buildings have less than 6 rooms. 10 buildings have more than 7 rooms. (EXTRA INFORMATION) 4 buildings have more than 8 rooms. ANSWER Therefore, 25 - 10 - 4 = 11 buildings that have 6, 7, or 8 rooms. A blind man is handed a deck of 52 Cards and told that exactly 10 of these cards are facing up.
How can he divide the cards in two piles (possibly of different sizes) having the same number of cards facing up? Solution The blind-folded man divides the cards into two piles with 10 and 42 cards each. He then flips all cards in the smaller pile. Done! If you roll three fair six-sided dice, what is the probability that the product of the three numbers rolled is even?
A) 1/8 B) 1/6 C) 1/2 D) 5/6 E) 7/8 ANSWER: Choice E (7/8) 1) The total number of possible outcomes of rolling three fair six-sided dice would be 216. This is because there are 6 outcomes for each dice (6*6*6 = 216) 2) First off...the word "Product" indicates the result from multiplication. So, we are going to look at possible Multiplication Outcomes: (EVEN #)*(EVEN #)*(EVEN #) = EVEN# (ODD #)*(EVEN #)*(EVEN #) = EVEN# (ODD #)*(ODD #)*(EVEN #) = EVEN# (ODD #)*(ODD #)*(ODD#) = ODD# ---> The only way in multiply three numbers to get an odd number 3)It actually would be easier to find the probability of rolling three numbers with an "odd" product because there is only one way to multiply three numbers to get an odd number 4) On each of the three dice the only odd numbers are 1, 3, and 5. The total possible combinations with getting these three odd numbers is 3*3*3 = 27 possible combinations. Therefore, the probability of getting an odd product is 27/216, which reduces to 1/8. 5) Ergo, because the only other option is getting an even product, the probability of rolling three numbers with an even product is 1-1/8 = 8/8-1/8 = 7/8-->Choice E A square is cut into two equal rectangles, each with perimeter 36. Find the area of the square.
A) 36 B) 64 C) 100 D) 144 E) 196 ANSWER: Choice D-- 144 Angles are complements if they add to 90 degrees. Let Angle A be nine times Angle B and the complement of Angle B be nine times the complement of angle A. Find Angle B.
A) 6 degrees B) 8 degrees C) 9 degrees D) 10 degrees E) 12 degrees ANSWER: Choice C If A is the set of prime numbers and B is the set of 2 digit positive integers whose unit digit is 5, how many numbers are in common for both sets?
A) NONE B) ONE C) TWO D) SEVEN E) NINE ANSWER: Choice A Set A {1,3,5,7,11,13,17,19,......} --> Set of Prime Numbers (Numbers that have only two factors: "1" and "itself") Set B {15,25,35,45,55,......} -->Set of two digit positive integers whose unit digit (ones place) is "5" Each two digit positive integer with a unit digit of 5 has more than 2 factors, each of these numbers is Set B has 1, 5, and "itself" as a factor. Therefore these two sets are disjoint (sharing no common element). Therefore Choice A is the correct answer. If 75% of m is equal to k percent of 25, where k > 0, what is the value of m / k? (side note: " m / k " means "m divided by k")
ANSWER: m / k = 1/3 ANSWER:
The two triangles have close, but not quite the same slope. The 5x2 triangle has a rise of 0.4 while the 8x3 triangle has a rise of 0.375, a fact cleverly hidden by the fact that the lines are all bold in the figure. The result is that the hypotenuse of the full 13x5 triangle (slope 0.385) is not perfectly straight. On the top figure it is slightly concave, on the bottom it is slightly convex, just to enough to free up one square. From Wheaton Warrenville South High School What is the integer that satisfies the following three conditions:
1249 |
Math Problem of the Day ANSWERS PART II
Here are the solutions to The Math Problems of The Day. The problems and solutions shown here come
from a variety of sources and I attempt to vary the difficulty level of
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