A bag contains 8 pounds of nuts, and 1/3 of the nuts, by weight, are walnuts.If 3 pounds of walnuts are added to the bag, what will be the fraction of the nuts in the bag, by weight, that are walnuts?
Answer(s): A
Originally, the bag holds total nuts: 8 lb walnuts: 1/3 × 8 = 8/3 lbAfter adding 3 lb of walnuts:new total weight: 8 + 3 = 11 lb new weight of walnuts: 8/3 + 3 = 8/3 + 9/3 = 17/3 lb.Hence the fraction of the nuts that are walnuts is:
Carlos owns twice as many books as Surya and one-third as many books as Ian. Ian owns 10 more books than Emma.Which of the following statements individually provide(s) sufficient additional information to determine how many books Carlos owns?Indicate all such statements.
Answer(s): A,B,C
Let's Carlos is C, Surya is S, Ian is I, and Emma is E.From the given information: C = 2S, I = 3C, and E = I - 10 = 3C - 10.Emma owns 5 times as many books as Surya:Emma owns 50 books. Then 50 = 3C - 10 C = 20.Emma owns 30 more books than Carlos. Then C + 30 = 3C - 10 C = 20.Therefore, all statements are sufficient.
Cylindrical can A contains five servings of soup when full. How many servings of the soup are contained in a full cylindrical can with 2 times the diameter and 3 times the height of can A?
Answer(s): B
Volume of a cylinder is proportional to (diameter)2 × height (since radius scales with diameter).New can: diameter × 2 volume × (22 ) = × 4; height × 3 volume × 3.Total volume scale factor = 4 × 3 = 12.Servings scale the same way: 5 × 12 = 60.
A subway train travels a straight route from Station S to Station T, making three stops along the route. The distance from S to the first stop is 1/4 of the distance from S to T. The distance from the first stop to the second stop is 1/3 of the distance from the first stop to T. The distance from the second stop to the third stop is 2/3 of the distance from the second stop to T. The distance from the first stop to the second stop is what fraction of the distance from the first stop to the third stop?
Let the total distance from S to T be 1. Then
At 9:00 A.M. trains X and Y were 200 miles apart, and they were traveling toward each other along adjacent parallel tracks. The engineer of train X maintained a constant speed of 60 miles per hour and the trains passed each other at 10:30 A.M.Quantity AThe average speed at which train Y traveled between 9:00 A.M. and 10:30 A.M.Quantity B60 miles per hour
From 9:00 to 10:30 is 1.5 hours.The trains together cover 200 miles in 1.5 hours, so their combined speed isTrain X speed is 60 mph, so Train Y average speed isSo, Quantity A is greater.
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