Hi Puys,
I have a few PS queries. These questions r from the Official Guide Quantitative Review...I don't have the answer explantions, only the answer key...
Thanks in advance...
Below r the questions:
191) The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of the six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has maximum value?
A) 3 B) 4 C) 5 D) 6 E) 8
196) The ratio, by volume, of soap to alcohol in a certain solution is 2:50:100. The solution will be altered so that the ration of the soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimetres of alcohol, how many cubic centimetres of water will it contain?
a)50 b) 200 c) 400 d) 625 e) 800
220) John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?
a)4y b) 5y c) 6y d) 8y e) 9y
234) In a certain game, a large container is filled with red, yellow, green and blue beads worth respectively, 7, 5, 3, 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
a)5 b) 4 c) 3 d) 2 e) 0
23
Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y- coordinates of P,Q, and R are to be integers that satisfy the inequalities -4
a)110 b) 1100 c) 9900 d) 10000 e) 12100
Answers
Q 191) B
Q 196) E
Q 220) E
Q 234) D
Q 23 A
191.
consider the cuboid...u hv three diff. rectangles - 6x8, 8x10 and 6x10 tht form the faces of the cuboid...if the cylinder rests on the 6x8 rectangle, then the max. diameter it can hv is 6 inches and max. height is 10 inches..hence volume = 90pi
when u consider 8x10 face, max dia = 8 in. and max vol = 96pi
when u consider 6x10 face, max dia = 6 in. and max vol = 72pi
hence, max vol = 96pi when dia = 8 in. i.e.
radius = 4 inches
196.
missing data - ratio of soap:alcohol:
water = 2:50:100
whenever a ratio is doubled or halved, u double or halve the first quantity of the ratio.
hence, soap:alcohol = 4:50
soap:water = 1:100
since it contains 100 cc of alcohol, amt. of soap = 8 cc. hence
amt. of water = 800 cc.
220.
both were given x dollars in advance. let us assume their hourly wage be 'a' dollars.
thus, if john worked for 10 hrs, he shud get 10a dollars and mary shud get 8a dollars.
now, mary gave y dollars to john. hence, amt. left with mary = x-y. this is equal to the total wage tht she gets
therefore x-y = 8a
john gets x+y dollars. thus x+y = 10a
solving both the equations, u get
x=9y.234.
since we need to find only how many red beans were removed, we need to find hw many times 7 occurs as a factor of 147000...
147 = 49x3 = 7x7x3
thus, there were
2 red beans removed.
23_.
consider pt.P.. within the range -4 to 5 for x co-ordinate, it can have 10 values...similarly, for y co-ordinate, it can have values frm 6 to 16 i.e. 11 values...thus a total of 110 possible co-ordinate values.
now, R will hv the same y co-ordinate as P...hence, y co-ordinate of R can have 9 values (1 value is already assigned to P amongst the original 10 values)
similarly, Q will hv same X co-ordinate.hence, Q can have 10 values for x co-ordinate.
thus, total no. of triangles = 110 x 9 x 10 =
9900...i think this is the right answer and
not 110...plz tell me if i am right or wrong...
??:
Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y- coordinates of P,Q, and R are to be integers that satisfy the inequalities -4