mathewhe/aqua_rat huggingface dataset:
Question: A shipment of 230 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
(A) 1/250
(B) 1/84
(C) 1/11
(D) 9/68
(E) 1/3
Rationale: Probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = (84/230)
Probability of chosing one defective phone from a lot of 229(we already picked one) which ontains 83(we already picked one) defective phones is = (83/229)
Combined probability of series of events = product of the probabilities = (84/230)*(83/229)
84/230 is close to (23/63) and (83/229)= (29/80)
so answer is (23/63)*(29/80) = (9/68)
So, answer will be D
Answer: (D) 9/68
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.54 more than Jane, what was the original price of the dish?
(A)  24
(B)  34.8
(C)  36
(D)  42
(E)  84
Rationale: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.54 --> 15p - 13.5p = 54 --> p = 36.
Answer: C.
Answer: (C)  36
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 372
(B) 375
(C) 278
(D) 267
(E) 288
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer:B
Answer: (B) 375
Question: Mixture A is 25 percent milk, and mixture B is 65 percent milk. If the two are poured together to create a 4-gallon mixture that contains 40 percent milk, approximately how many gallons of mixture A are in the mixture?
(A) 1.5
(B) 1.75
(C) 2.85
(D) 2.5
(E) 3.0
Rationale: (65-40)/(40-25) = Qa/Qb
25/15 = Qa/Qb
5/3 = Qa/Qb
Qa = (5/7) * 4 = 20/7 = 2.85 approx
Answer : C
Answer: (C) 2.85
Question: In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score K that Lindsey could have received on her midterm exam?
(A) 52%
(B) 64%
(C) 72%
(D) 76%
(E) 80%
Rationale: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Answer: (A) 52%
Question: There are 11 dozen mangoes in a box. If there are 16
such boxes, how many mangoes are there in all the
boxes together?
(A) 2112
(B) 3096
(C) 6192
(D) 628
(E) None
Rationale: Number of mangoes = 11 dozens
= 11 × 12 = 132
∴ Number of mangoes in 16 boxes
= 16 × 132 = 2112
Answer A
Answer: (A) 2112
Question: The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 26
(C) 27
(D) 28
(E) 22
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 60 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (60 + 20) / 2 = 40.Answer:a
Answer: (A) 40
Question: A shipment of 250 smartphones contains 67 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
(A) 1/250
(B) 1/14
(C) 1/11
(D) 1/9
(E) 1/3
Rationale: Probability of chosing one defective phone from a lot of 250 which ontains 67 defective phones is = (67/250)
Probability of chosing one defective phone from a lot of 249(we already picked one) which ontains 66(we already picked one) defective phones is = (66/249)
Combined probability of series of events = product of the probabilities = (67/250)*(66/249)
67/250 is close to (26/97) and (66/249)= (22/83)
so answer is (26/97)*(22/83) = (1/14)
So, answer will be B
Answer: (B) 1/14
Question: If x+y=24, x-y=40, for integers of x and y, x=?
(A) 20
(B) 23
(C) 25
(D) 32
(E) 42
Rationale: x+y = 24
x-y = 40
2x = 64
x = 32
Answer is D
Answer: (D) 32
Question: A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $14000 left with him. find salary..
(A) $10400
(B) $14000
(C) $144000
(D) $1800
(E) $140000
Rationale: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount
[1-(1/5 + 1/10 + 3/5)} * total salary= $14000, = [1-9/10] * Total salary = $14000, Total salary = $14000*10 = $140000, correct answer (E)
Answer: (E) $140000
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 90 ps per meter is?
(A) 287
(B) 369
(C) 225
(D) 279
(E) 361
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 0.9
= Rs.225
Answer:C
Answer: (C) 225
Question: A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.
(A) 360, 160, 200
(B) 160, 360, 200
(C) 200, 360,160
(D) 200,160,300
(E) 300,260,100
Rationale: let ratio be x.
Hence no. of coins be 5x ,9x , 4x respectively
Now given total amount = Rs.206
=> (.50)(5x) + (.25)(9x) + (.10)(4x) = 206
we get x = 40
=> No. of 50p coins = 200
=> No. of 25p coins = 360
=> No. of 10p coins = 160
Answer:C
Answer: (C) 200, 360,160
Question: There is a total of 100 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/5. What is the probability that the marble will be either red or blue?
(A) 2/3
(B) 3/5
(C) 7/10
(D) 9/20
(E) 11/20
Rationale: P(red or blue) = 1 - P(white) - P(green) = 20/20 -5/20 - 4/20 = 11/20
The answer is E.
Answer: (E) 11/20
Question: A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
(A) 1,250 meters / minute
(B) 1,760 meters / minute
(C) 1,443 meters / minute
(D) 1,980 meters / minute
(E) 1,667 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
75 kilometers per hour = 75 km/hr
= (75 × 1000 meters) / (60 minutes) = 1,250 meters / minute
correct answer A
Answer: (A) 1,250 meters / minute
Question: A man swims downstream 36 km and upstream 18 km taking 6 hours each time, what is the speed of the man in still water?
(A) 4.5
(B) 5.5
(C) 6.5
(D) 4.8
(E) 2
Rationale: 36 --- 6 DS = 6
? ---- 1
18 ---- 6 US = 3
? ---- 1 M = ?
M = (6 + 3)/2 = 4.5
Answer: A
Answer: (A) 4.5
Question: The product of 4 consecutive even numbers is always divisible by:
(A) 600
(B) 768
(C) 864
(D) 384
(E) 356
Rationale: To solve this question, we need to know two facts.
Fact 1:
The product of 4 consecutive numbers is always divisible by 4!.
Fact 2:
Since, we have 4 even numbers, we have an additional 2 available with each number.
Now, using both the facts, we can say that the product of 4 consecutive even numbers is always divisible by,
=(24)×4!=(24)×4!
=16×24=16×24
=384
Option(D)
Answer: (D) 384
Question: If 4d^4 − 41d^2 + 100 = 0, then what is the sum of the two greatest possible values of d ?
(A) 4
(B) 9/2
(C) 7
(D) 41/4
(E) 25
Rationale: just forget about the value of d^4 for the moment and let d^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so d^2 = 4 and 25/4
so d= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
Answer: (B) 9/2
Question: According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 320 6 ounces servings of orange juice?
(A) a) 25
(B) b) 34
(C) c) 50
(D) d) 40
(E) e) 100
Rationale: Its D.
Total juice rquired = 320*6 = 1920 ounce
12 ounce concentate makes = 12 * 4 = 48 ounce juice
Total cans required = 1920/48 = 40.
Answer D
Answer: (D) d) 40
Question: A circular ground whose diameter is 70 metres, has a 2.8 metre-broad garden around it. What is the area of the garden in square metres?
(A) 540.72
(B) 740.64
(C) 640.64
(D) 620.45
(E) 725.26
Rationale: Req. area = Ï€[(37.8)2 â€“ (35)2]
= 22â„7 Ã— (72.8 Ã— 2.8)[since a2 - b2 = (a + b)(a - b)]
= 22 Ã— 72.8Ã— 0.4 = 640.64 sq m
Answer C
Answer: (C) 640.64
Question: R is the set of positive odd integers less than 10, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A) None
(B) Two
(C) Four
(D) Five
(E) Seven
Rationale: squares < 10 {1,4,9}
S = {1,9}
R = {1,3,.....10}
Hence B.
Answer: (B) Two
Question: The average of first five multiples of 5 is :
(A) 3
(B) 9
(C) 12
(D) 15
(E) 17
Rationale: Solution
Average = 5(1+2+3+4+5)/5 =75/5 =15 Answer D
Answer: (D) 15
Question: Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.35 per ounce, what is the share of Arabica in this blend?
(A) 20%
(B) 24%
(C) 50%
(D) 33%
(E) 40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.4a + .3(1-a) = .35
.4a + .3 - .3a = .35
a= .5
therefore: .5/1 ounce = 50%. Therefore, the answer should be C
Answer: (C) 50%
Question: Find the area of a cuboid of length 4cm , breadth 6 cm . and height 5cm.
(A) 120 cm cube
(B) 110 cm cube
(C) 220 cm cube
(D) 430 cm cube
(E) 480 cm cube
Rationale: Area of a cuboid = lxbxh =4cm x 6cm x 5cm = 120 cm cube
answer :A
Answer: (A) 120 cm cube
Question: If all the sides of a right triangle increase in length by 10%, then by what percentage does the area of the triangle increase?
(A) 21%
(B) 42%
(C) 80%
(D) 96%
(E) 120%
Rationale: Let B be the base and H be the height of the original triangle.
The original area is (1/2)BH.
The area of the expanded triangle is (1/2)(1.1B)(1.1H) = (1.1)(1.1)(1/2)BH = 1.21(1/2)BH
The answer is A.
Answer: (A) 21%
Question: A person takes 10 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
(A) 50 minutes
(B) 20 minutes
(C) 40 minutes
(D) 60 minutes
(E) 80 minutes
Rationale: Let the distance and original speed be d km and k kmph respectively.
d/0.8k - d/k = 10/60 => 5d/4k - d/k = 1/6
=> (5d - 4d)/4k = 1/6 => d = 4/6 k=2/3k
Time taken to cover the distance at original speed
= d/k = 2/3 hours = 40 minutes.
ANSWER:C
Answer: (C) 40 minutes
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 17 miles per hour." What was their average speed in the whole journey?
(A) 10 miles/hour
(B) 12 miles/hour
(C) 11 miles/hour
(D) 12.6 miles/hour
(E) 14 miles/hour
Rationale: 2xy/x+y=12.6 miles/hour
ANSWER:D
Answer: (D) 12.6 miles/hour
Question: A certain city with a population of 144,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 12,000
(B) b) 10,800
(C) c) 10,900
(D) d) 11,000
(E) e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 144k
x = 12,000
Answer : A
Answer: (A) a) 12,000
Question: calendar=52097083 november=538=8651
march=2*308 blue=7154 december=?
(A) 9535&153
(B) 9585&153
(C) 9525&153
(D) 9525&*53
(E) 9525&*54
Rationale: from above in formation
d=9
e=5
c=2
e=5
m=3
b=1
e=5
r=8
95253158( Order doesnot matter i guess!)
another thing is &=8 for mathcing above ans
ANSWER:C
Answer: (C) 9525&153
Question: How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 3%?
(A) 0—1.5 gal
(B) 1.5—3 gal
(C) 3—4.5 gal
(D) 4.5—6 gal
(E) 16+ gal
Rationale: Let amount of water that must be added in gallons to dilute concentration of brine solution = x
Amount of brine already present = 10/100 * 10 = 1 gallon
1/(10+x) *100 = 3
=>100 = 30 + 3x
=> x= 70/3 = 23
Answer E
Answer: (E) 16+ gal
Question: Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?
(A) 6 hrs
(B) 6 2/3 hrs
(C) 7 hrs
(D) 7 1/2 hrs
(E) 8 hrs
Rationale: Explanation:
(A + B)'s 1 hour work = (1/12 + 1/15) = 3/20
(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = 3 * 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs.
ANSWER IS C
Answer: (C) 7 hrs
Question: A runs 5/2 time as fast as B, and gives B and a start of 40m. How long should the racecourse be so that A and B might reach in the same time?
(A) 150 m
(B) 100 m
(C) 75 m
(D) 80 m
(E) 90 m
Rationale: verification of options..... (2/5)*100 =40
So answer is 100m
ANSWER:B
Answer: (B) 100 m
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the R odds that it is an ace?
(A) 1/52
(B) 1/26
(C) 1/13
(D) 1/4
(E) 5/13
Rationale: The question should ask about the probability not the odds.
There are 13 spades, the probability R that the spade we already have is an ace is therefore 1/13.
Answer: C.
Answer: (C) 1/13
Question: In a 200 m race,A covers the distance in 45 seconds and B in 60 second.In this race A beats B by :
(A) 20 m
(B) 50 m
(C) 45 m
(D) 60 m
(E) None of these
Rationale: Solution
Distance covered by B in 15 sec. = (200/60x15)m =50m.
∴ A beats B by 50 metres.
Answer B
Answer: (B) 50 m
Question: Ram professes to sell his goods at the cost price but he made use of 850 grms instead of a kg, what is the gain percent?
(A) 11 1/7%
(B) 11 7/7%
(C) 11 1/9%
(D) 17.64%
(E) 11 1/2%
Rationale: 850 --- 150
100 --- ? => 17.64%
Answer:D
Answer: (D) 17.64%
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
(A) Rs. 8000
(B) Rs. 9000
(C) Rs. 9900
(D) Rs. 9990
(E) Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: (E) Rs. 10000
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm?
(A) 320cm2
(B) 280cm2
(C) 384cm2
(D) 290cm2
(E) 350cm2
Rationale: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm.
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 24 x 32) cm2 = 384 cm2
hence C
Answer: (C) 384cm2
Question: A person starting with Rs.64 and making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for 1/2 the money remaining at the time of the bet, then the final result is?
(A) Rs.23
(B) Rs.37
(C) Rs.45
(D) Rs.67
(E) Rs.77
Rationale: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
B
Answer: (B) Rs.37
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.7
II. 12.3
III. 9.5
(A) I only
(B) I and II only
(C) II only
(D) III only
(E) I and III only
Rationale: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
12.3 and 9.5 lies in the range of 2SD from mean
Answer: Option A
Answer: (A) I only
Question: Susan has nine hamsters. In order to feed each hamster 4 blocks of food each day, how much food must she buy for 7 days?
(A) 210
(B) 228
(C) 243
(D) 252
(E) 271
Rationale: 4 blocks of food per day multiplied by 9 hamsters = 36 blocks per day. 36 multiplied by 7 days = 252 blocks of food, hence answer : D.
Answer: (D) 252
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
(A) 2287
(B) 2689
(C) 1667
(D) 8112
(E) 1691
Rationale: A = 7500(26/25)2 = 8112
Answer: D
Answer: (D) 8112
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 7% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
(A) 2
(B) 5
(C) 700/107
(D) 110/20
(E) 9/4
Rationale: Let price be 10/ticket
then 220 tickets for this month's performance at its usual price=2200
which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000
now new revenue this month=200*10.7=2140
as per question asked 2000=2140(1-A/100)----->A=700/107%
Ans C
Answer: (C) 700/107
Question: The circumferences of two circles are 264 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 29960 sq m
(B) 33880 sq m
(C) 43120 sq m
(D) 27680 sq m
(E) 12786 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 704
s = 264/2∏ and l = 704/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{132^2/∏^2 - 352^2/∏^2}
= 132^2/∏ - 352^2/∏
= (132 - 352)(132 + 352)/∏
= (220)(484)/(22/7)
= 33880 sq m
Answer:B
Answer: (B) 33880 sq m
Question: If |x – 9/2| = 5/2, and if y is the median of a set of t consecutive integers, where t is odd, which of the following must be true?
I. xyt is odd
II. xy(t^2 + t) is even
III. x^2y^2t^2 is even
(A) II only is true
(B) III only is true
(C) I and III
(D) II and III
(E) I, II, and III
Rationale: given:
t is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: t = O, y = O and x = O or E
Statement I = x*y*t = y*t*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(t^2 + t) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2t^2 is even. E/O x O x O = Odd or even. Hence False.
Answer = A.
Answer: (A) II only is true
Question: The ratio of ages of two friends is 3:5 and sum of their ages is 80 years. What are their present ages in years?
(A) 10,60
(B) 20,60
(C) 40,30
(D) 30,50
(E) 20,50
Rationale: 3x + 5x== 80
x==10
(30,50)
ANSWER:D
Answer: (D) 30,50
Question: The table below shows how many coaches work with each of the major sports teams at Kristensen School. Although no single coach works with all three teams, 3 coaches work with both the Track and Tennis teams, 2 coaches work with both the Track and Baseball teams, and 1 coach works with both the Tennis and Baseball teams. How many different coaches work with these three teams?
Sports No of coaches
Track 8
Tennis 7
Baseball 4
(A) 6
(B) 9
(C) 11
(D) 13
(E) 17
Rationale: X = 8 + 7 + 4 - (3 + 2 + 1) = 13
Answer is D
Answer: (D) 13
Question: At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
(A) 5 1/11 °
(B) 12 4/11 °
(C) 13 4/11°
(D) 16 4/11°
(E) None
Rationale: Solution
At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.
15 min. are gained in
= (60/55 x 15)min
=16x4/11
The hands are coincident at 16x4/11 min past3.
Answer D
Answer: (D) 16 4/11°
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 80 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
(A)  100
(B)  120
(C)  140
(D)  150
(E)  160
Rationale: Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+80)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=160
Ans E
Answer: (E)  160
Question: The diagonal of a cube is cm. Find its surface area
(A) 216 sq.cm
(B) 316 sq.cm
(C) 416 sq.cm
(D) 516 sq.cm
(E) None of these
Rationale: Explanation:
Let the edge of the cube be a.
so, the diagonal √3 a = 6√3
=> a=6
Surface area = 6a2 = 6 x 6 x 6 = 216 cm2
Answer: A
Answer: (A) 216 sq.cm
Question: The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be maths teachers?
(A) 2/3
(B) 1/3
(C) 2/9
(D) 1/24
(E) 1/12
Rationale: Probability of first member an English teacher = 3/9
Probability of second member an English teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (E)
Answer: (E) 1/12
Question: Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 40 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?
(A) 36
(B) 72
(C) 132
(D) 144
(E) 180
Rationale: 1st part: - In 1hr, Bus A covers 30 miles.
Relative speed of bus ABus B is (80-30) = 50mph.
So time required for Bus B to cover the exact distance as A is
50*t = 30
t=3/5 = 36min
2nd part
80*t=2d - B has to cover twice the distance
30*(t+1) = d - A traveled 1hr more and has to travel only only d
so
d/30 - 2d/80 = 1
D=120
T= 3hrs = 180 min
Question asks for +ve difference between part 1 and part 2 in minutes
= 180-36 = 72min
B
Answer: (B) 72
Question: A family pays $700 per year for an insurance plan that pays 70 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?
(A) $1,100
(B) $1,300
(C) $1,400
(D) $1,800
(E) $2,200
Rationale: Assuming the medical expenses are $1000 or more, the family pays $700 + $300 = $1000.
The total amount paid by insurance plan for the first $1000 of expenses is $700.
The insurance will pay another $300 when the medical expenses are $1300.
The answer is B.
Answer: (B) $1,300