GMAT Quantitative Problem Solving.docx

GMAT Quantitative: Problem Solving 1. Two travelers are trying to estimate their travel time by using a map. On the map, a distance of 3cm represents an actual distance of 45km. On the map, the distance between their initial location and their destination is 55cm. How far will they have to travel? A) 600km  B) 750 km  C) 825 km  D) 925 km  E) 1000 km Correct Answer: C Explanation: First, it is necessary to convert km to cm. 1 km=100,000cm. So, 45km x 100,000cm = 4,500,000cm. Next, a ratio can be set up: 3cm/4,500,000cm = 550cm/x Using cross multiplication: 3x=247,500,000 To find x: x=247,500,000/3 x=82,500,000cm To get this value in kilometers, it is necessary to divide the value by 100,000. 82,500,000/100,000=825km 2. A company has increased its monthly profits from $12,500 to $17,800. By what percentage did their profits increase? A) 29.3%  B) 36.7%  C) 42.4%  D) 53.9%  E) 61.2% Correct Answer: C Explanation: First, find the actual change in their profits: (17,800 - 12,500 = 5300) Then, calculate the percent increase this represents: 5300/12,500(the initial amount)=0.424 or 42.4 %. 3. A triangle has a base of 7cm and a height of 13cm. If the base is reduced to 4cm, by how much will the area of the triangle decrease? A) 7cm  B) 10.5 cm  C) 15 cm  D) 19.5 cm  E) 24 cm Correct Answer: D Explanation: First, calculate the area of the original triangle: (1/2[7*13]=45.5cm) Then calculate the area of the second triangle: (1/2[4*13]=26cm) Finally, calculate the difference between the two areas: (45.5cm-26cm=19.5cm) 4. Which of the following represents the greatest value? A) 35 + 65%  B) 25% of 65 + 3  C) 50.5 / 22  D) 0.22 x 300 + 5%  E) 230.7/0.7 Correct Answer: E Explanation: To solve this problem, it is simply necessary to calculate each value. A=57.75  B=19.25  C=12.63  D=69.3  E=329.57 E represents the greatest value. 5. If 5p-t=56 and 2t+24=60, what is the value of p? A) 11.8  B) 12.8  C) 13.8  D) 14.8  E) 15.8 Correct Answer: D Explanation: By using the second equation, the value of t can be calculated. 2t=60-24  2t=36  t=36/2  t=18 Then, it is simply a matter of substituting 18 in for t to calculate p 5p-t=56  5p-18=56  5p=56+18  5p=74  p=74/5  p=14.8