mathewhe/aqua_rat huggingface dataset:
Question: A package contains 8 black and 10 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 3/5
(B) 5/9
(C) 6/8
(D) 7/9
(E) 1/3
Rationale: Let number of balls = (8+10) = 18.
Number of white balls = 10.
P (drawing a white ball) =	10/18	=	5/9
B
Answer: (B) 5/9
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/37
(C) 31/18
(D) 31/10
(E) 31/19
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: A
Answer: (A) 31/32
Question: When positive integer B is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
(A) a. k + 1
(B) b. k -11
(C) c. 4k + 2
(D) d. (k-3)/3 +2
(E) e. B/3
Rationale: When positive integer B is divided by 6 the remainder is 3
So, B could equal 3, 9, 15, 21, etc
let's TEST B =3
a.3+ 1 = 4 (EVEN)
b.3-11 = -8 (EVEN)
c. 4(3) + 2 = 14 (EVEN)
d. (3-3)/3 +2 = 2 (EVEN)
At this point, we can already see the answer must be E.
Let's check E forfun
e.3/3 = 1 (ODD)
Great!
Answer: E
Answer: (E) e. B/3
Question: If an average hard drive had a capacity of 0.2 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
(A) 256
(B) 5122
(C) 768
(D) 2048
(E) 1536
Rationale: 0.2*2^10=0.2*1024=204.8
The answer is D.
Answer: (D) 2048
Question: A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?
(A) 40
(B) 45
(C) 50
(D) 90
(E) 2500
Rationale: First recognize you only need to consider the first two digits (because the second two are just the first two flipped)
There are 90 possibilities for the first two digits of a 4 digit number, 10-99 inclusive. Everything starting with a 1,3,5,7,9 will be odd, which is 5/9ths of the combinations.
5/9*90 = 50
ANSWER:C
Answer: (C) 50
Question: A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the R % profit made by the merchant?
(A) 66.67 %
(B) 50 %
(C) 200 %
(D) 100 %
(E) 33.33 %
Rationale: C.P of 1 article= $30(say)
C.P of 20 articles=30*20=$600
Now, C.P of 20 articles=Profit on 30 articles
Therefore, profit on 1 article=$600/30=$20
Profit R%=(20/30)*100=66.67%
Answer A
Answer: (A) 66.67 %
Question: If 3 men or 4 women can reap a field in 43 days how long will 7 men and 5 women take to reap it?
(A) 9
(B) 12
(C) 15
(D) 18
(E) 19
Rationale: Explanation:
3 men reap 1/43 field in 1 day
1 man reap 1/(3 x 43)
4 women reap 1/43 field in 1 day
1 woman reap 1/(43 x 4)
7 men and 5 women reap (7/(3 x 43)+ 5/(4 x 43)) =1/12 in 1 day
7 men and 5 women will reap the field in 12 days
Answer: Option B
Answer: (B) 12
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 840?
(A) 15
(B) 48
(C) 64
(D) 84
(E) 105
Rationale: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)
840 = 8*3*5*7
The GCF could be 12 or 84.
The answer is D.
Answer: (D) 84
Question: A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 10 books for a total of $42.00, and on Tuesday the store sold 20 maps and 15 books for a total of $70.00. At this store, how much less does a map sell for than a book?
(A)  $0.25
(B)  $0.50
(C)  $3.5
(D)  $2.5
(E)  $l.25
Rationale: 12x+10y=42
20x+15y=70
multiply eq 1 by 5 and eq 2 by 3
60x+50y=42*5
60x+45y=70*3
subtracting 1 from 2
5y=210-210
y=0
therefore
x=3.5
difference in price =3.5
C
Answer: (C)  $3.5
Question: There are 12 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
(A) 132
(B) 145
(C) 165`
(D) 400
(E) 300
Rationale: The total number of stations= 12
From 12 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 12P2 ways.
12P2= 12*11= 870
ANSWER:A
Answer: (A) 132
Question: courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?
(A) 22
(B) 77
(C) 877
(D) 99
(E) 88
Rationale: 3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7
5.25 meters=525 cm = 5 × 5 × 3 × 7
Hence common factors are 3 and 7
Hence LCM = 3 × 7 = 21
Hence largest size of square tiles that can be paved exactly with square tiles is 77 cm.
Answer:B
Answer: (B) 77
Question: 750 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
(A) a) 162
(B) b) 15
(C) c) 60
(D) d) 38
(E) e) 12
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 750 = 15
Answer: B
Answer: (B) b) 15
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) m
(B) m
(C) m
(D) m
(E) m
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
ANSWER:D
Answer: (D) m
Question: The difference between the simple interest received from two different sources on Rs. 500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
(A) A)2.4%
(B) B)6.6%
(C) C)0.3%
(D) D)2.0%
(E) E)1.3%
Rationale: (500 * R1 * 3)/100 - (500 * R2 * 3)/100 = 13.50 1500(R1 - R2) = 1350
R1 - R2 = 6.6%
Answer:B
Answer: (B) B)6.6%
Question: IF n >0 what is the remainder when 912^n+3 is divided by 10
(A) 0
(B) 1
(C) 2
(D) 7
(E) 9
Rationale: For every even power, units digit of 9 will be 1 and for every every odd power units digit of 9 will be 9.
Since expression 12n+3 is odd, the units digit will be 9, which will also be the reminder when the expression is divided by 10.
E is the answer
Answer: (E) 9
Question: The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
(A) 5/7
(B) 12/35
(C) 2/47
(D) 8/9
(E) 7/5
Rationale: Explanation:
Let the numbers be a and b. Then, a + b = 12 and ab = 35
a+b/ab=12/35
(1/b+1/a)=12/35
Sum of reciprocals of given numbers=12/35
ANSWER:B
Answer: (B) 12/35
Question: If m/49 is an integer, then each of the following must be an integer EXCEPT
(A) 4
(B) 3
(C) 9/2
(D) 4
(E) 5
Rationale: Now plug m =49 into the answer choices:
A. (49- 28)/7 =3This is an integer
B. (49+ 21)/7 = 10. This is an integer
C. 14(49)/98 = 7. This is an integer
D. (49^2 - 49)/49 =48. This is an integer
E. (49+ 14)/14 = 9/2. This is NOT an integer
Answer: C
Answer: (C) 9/2
Question: If x and y are positive integers, and x^3*y^4 = 432, which of the following is the value of xy?
(A) 6
(B) 10
(C) 14
(D) 15
(E) 21
Rationale: 432 = 2*216 = 2^2*108 = 2^3*54 = 2^4*27 = 2^4*3^3
xy = 2*3 = 6
The answer is A.
Answer: (A) 6
Question: 20 women can do a work in 9 days. After they have worked for 6 days. 6 more men join them. How many days will they take to complete the remaining work?
(A) 4:7
(B) 4:3
(C) 4:2
(D) 4:0
(E) 4:1
Rationale: (20 * 16) women can complete the work in 1 day.
1 woman's 1 day work = 1/320
(16 * 15) men can complete the work in 1 day
1 man's 1 day work = 1/240
So, required ratio = 1/240 : 1/320 = 4:3.
Answer: B
Answer: (B) 4:3
Question: What is the area S of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?
(A) 60.
(B) 85.
(C) 125.
(D) 225.
(E) It cannot be determined from the information given
Rationale: Length of one side= 15 (20-5)
Since, its a square, the area will be S= 15^2= 225
D is the answer
Answer: (D) 225.
Question: The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
(A) 24 cm
(B) 17 cm
(C) 14 cm
(D) 10 cm
(E) 12 cm
Rationale: Side of first square = (40/4) = 10 cm;
Side of second square = (32/4)cm = 8 cm.
Area of third square = [(10) 2 - (8) 2] cm2 = (100 - 64) cm2 = 36 cm2.
Side of third square = (36)(1/2) cm = 6 cm.
Required perimeter = (6 x 4) cm = 24 cm.
ANSWER A 24cm
Answer: (A) 24 cm
Question: The payment per hour for a daily-wages employee is increased by 33.33 and the working time is reduced by 33.33%. What is the percentage change in the employee's income?
(A) Rs. 0.7889
(B) Rs. 0.8889
(C) Rs. 0.9889
(D) Rs. 1.8889
(E) Rs. 2.8889
Rationale: If payment per hr is increased by 33.33 % , then
11.11 % decrease in income
If earlier he is getting Rs 1 hr per hr and working for 1 hr, income = Rs 1
Now he is getting Rs 1.3333 per hr and working for 0.66667 hrs, income = Rs. 0.8889
ANSWER:B
Answer: (B) Rs. 0.8889
Question: The sides of a cube are in the ratio 1:2 the ratio of their volume is?
(A) 1:9
(B) 1:7
(C) 1:8
(D) 1:6
(E) 1:4
Rationale: 1:8
Answer: C
Answer: (C) 1:8
Question: Nine pens are in the table.To create three pens in each group like as three group. How many ways are there to create these 3 teams?
(A) 27
(B) 45
(C) 90
(D) 175
(E) 280
Rationale: Arrange the 6 pen in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (B)
You get 6!/(2! * 2! * 2!) * 2!
Answer : B
Answer: (B) 45
Question: With a slope of 4, with a straight line in the xy- plane which has a point with x-coordinate of the point 14 and y-coordinate 19, find the y-intercept.
(A) -19
(B) 18
(C) -37
(D) 50
(E) 37
Rationale: Eq of line = Y = MX +C
M = 4
X= 14
Y= 19
C= Y - MX
Substitute given:
C= 19 - (4)(14)
C = -37
correct option is C
Answer: (C) -37
Question: A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 14 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
(A) 2
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: Let the speed be 's' and let the distance between rose and poppy be 'x'
The problem boils down to:
Rose to Poppy: s+3=x/6 ------- 1
Daisy to Rose: s=(x+14)/10------ 2
so from 1 we can re write x as x=6s+18
substitute the value of x in 2 gives us s=2 m/s
A
Answer: (A) 2
Question: If x+y=270, x-y=200, for integers of x and y, y=?
(A) 200
(B) 235
(C) 50
(D) 115
(E) 150
Rationale: x+y = 270
x-y = 200
2x = 70
x = 35
y = 235
Answer is B
Answer: (B) 235
Question: Subtracting 10% from X is the same as multiplying X by what number?
(A) 98%
(B) 90%
(C) 230%
(D) 97%
(E) 921%
Rationale: X - (10/100) X = X * ?
? = 90%
Answer:B
Answer: (B) 90%
Question: In a simultaneous throw of two coins the probability of getting at least one head is ?
(A) 3/4
(B) 1/2
(C) 1/4
(D) 2/3
(E) 1/5
Rationale: S={HH,HT,TH,TT}
E be the event of getting at least one head is {HT,TH,HH}
P(E)=n(E)/n(S)=3/4
Answer(A)
Answer: (A) 3/4
Question: 1,257
1,275
1,527
........
........
+7,521
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,5 and 7 exactly once in each integer. What is the sum R of the 24 integers ?
(A)  26,996
(B)  44,406
(C)  60,444
(D)  66,660
(E)  99,990
Rationale: This is the way i solved it :
Total no. of different combos = 24, total digits 4 therefore each digit must repeat 24/4 = 6 times in each row .. So the right most row would add up to 1x6 + 2x6 + 5x6 + 7x6 = 6+12+30+42 = 90 .. Each row would add up to 90, so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90+9 and 9 stays and one 9 goes to the row to the left, so the last two digits of the SUM R should be 90 (E) .. We could go on and solve the exact number but since only one answer choice has the last digits as 90 we needn't go any further..
Answer: (E)  99,990
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.60 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(A) 165
(B) 175
(C) 190
(D) 200
(E) 210
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.60 + X x 3.20 = 432
X = 5.
Hence, total hours of work = (160 + 5) = 165.
answer :A
Answer: (A) 165
Question: What least number must be added to 3000 to obtain a number exactly divisible by 19 ?
(A) 3
(B) 2
(C) 5
(D) 6
(E) 9
Rationale: EXPLANATION:
On dividing 3000 by 19, we get 17 as remainder.
Number to be added = (19 - 17) = 2
Answer B
Answer: (B) 2
Question: Jill is dividing her 12-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
(A) 10
(B) 25
(C) 462
(D) 252
(E) 630
Rationale: With 12 players, the process of figuring out how many groups of 6 can be formed is pretty straight-forward....
12C6 = 12!/(6!6!) = 924 possible groups of 6
Once forming that first group of 6, the remaining 6 players would all be placed on the second team by default.
The 'twist' is that the two teams of 6 canshow upin either order:
C
Answer: (C) 462
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 35% profit?
(A) 2000
(B) 2160
(C) 2299
(D) 2778
(E) 2771
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 135 % of Rs. 1600 = 135/100 * 1600 = Rs. 2160.
Answer:B
Answer: (B) 2160
Question: A bonus of Rs.2800 is to be divided among 3 people such that Alex gets twice as much as David, who receives one-fourth as much as Peter. What amount did Peter get?
(A) 1200
(B) 2000
(C) 1600
(D) 1500
(E) 1700
Rationale: Explanation:
Let Peter’s share be x.
Hence, David gets x/4 and Alex gets x/2.
x + x/4 + x/2 = 2800
7x/4 = 2800
x = Rs.1600
ANSWER C
Answer: (C) 1600
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip
was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the
flight ?
(A) 3 hours
(B) 2.4 hours
(C) 1.4 hours
(D) 1 hour
(E) None of these
Rationale: Explanation:
Let the duration of the flight be x hours.
Then
600x−600x+12=200600x−12002x+1=200x(2x+1)=32x2+x−3=0=>(2x+3)(x−1)=0
Neglecting the negative value for x we get x = 1
Answer: D
Answer: (D) 1 hour
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 72.Find the number of notes of Rs.50 denomination.
(A) 15
(B) 21
(C) 17
(D) 37
(E) 57
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 72 - X
Now,
50*X + 500 * (72 - X) = 10350
50X + 36000 - 500X = 10350
- 450X = - 25650
X = 57.
No. of 50 rupees note = 57.
Answer: Option E
Answer: (E) 57
Question: A vendor bought bananas at 6 for $10 and sold them at 4 for $6. Find his gain or loss percent?
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Rationale: Number of bananas bought = L.C.M of 6 and 4 = 12
C.P. = 10/6 * 12 = $20
S.P. = 6/4 * 12 = $18
Loss% = 2/20 * 100 = 10%
Answer is B
Answer: (B) 10%
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
(A) 20/60
(B) 20/63
(C) 20/69
(D) 20/61
(E) 20/611
Rationale: Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63
Answer: B
Answer: (B) 20/63
Question: A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 9:30 am in the same direction at the rate of 84 km/h. At what time will the second train catch the first train?
(A) 11:00
(B) 11:30
(C) 12:00
(D) 12:30
(E) 1:00
Rationale: In thirty minutes the first train travels 35 km.
The second train catches the first train at a rate of 84 km/h - 70 km/h = 14 km/h.
The second train will catch the first train in 35/14 = 2.5 hours, so at 12:00 noon.
The answer is C.
Answer: (C) 12:00
Question: A ladder 14 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 5 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?
(A) 4
(B) 5
(C) 8
(D) 10.72
(E) 15
Rationale: 14^2-5^2=171
it means that the height is equal to 13.07~=13.
since the top of the ladder slips down 4 feet, then the height of the wall =13-4=9
the bottom =sqrt(14^2-9^2)=sqrt(196-81)=10.72
ans is D
Answer: (D) 10.72
Question: An athlete runs 200 meters race in 10sec. His speed is?
(A) 20km/hr
(B) 15km/hr
(C) 30km/hr
(D) 72km/hr
(E) 40km/hr
Rationale: speed = 200/10 = 20 m/sec
= 20 * 18/5 km/hr = 72km/hr
Answer is D
Answer: (D) 72km/hr
Question: What is the compound interest paid on a sum of Rs.3000 for the period of 3 years at 10% per annum.
(A) 900
(B) 930
(C) 990
(D) 993
(E) None of these
Rationale: Solution= Interest % for 1st year= 10
Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11
Interest % for 3rd year= 10+ 10%(10+11)=10+ 2.1=12.1
Total % of interest= 10 + 11+12.1=33.1
Total interest = 33.1 % 3000= 3000 * (33.1/100)= 993
Answer D
Answer: (D) 993
Question: A ball is bought for Rs.400 and sold at a gain of 20% find its selling price
(A) Rs.400/-
(B) Rs.480/-
(C) Rs.500/-
(D) Rs.520/-
(E) Rs.540/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
B
Answer: (B) Rs.480/-
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $2,800 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $8,400 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
(A) 30%
(B) 35%
(C) 25%
(D) 40%
(E) 50%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 2800 : 8400 -----> 1 : 3
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 4) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/4) * 100 ---> 25%
Answer : C
Answer: (C) 25%
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $18. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 180xy
(B) 162/(xy)
(C) 20xy
(D) 20xy/9
(E) xy/180
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 18 / (xy/9) = 162/(xy).
The answer is B.
Answer: (B) 162/(xy)
Question: What is the difference between the place value of 2 in the numeral 7449?
(A) 360
(B) 165
(C) 180
(D) 190
(E) 200
Rationale: Answer: Option 'A'
400 - 40 = 360
Answer: (A) 360
Question: Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is :
(A) 17
(B) 29
(C) 36
(D) 48
(E) 58
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 60 or x = (60 * 4) / 5 = 48. Answer: D
Answer: (D) 48
Question: During a certain week, a seal ate 40% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
(A) 32
(B) 40
(C) 55
(D) 64
(E) 80
Rationale: Total smelt = x.
Then, 0.4*80+0.3(x-80)=0.4*x --> x=80 --> 0.4*x=32
Answer: A.
Answer: (A) 32
Question: If 14m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
(A) 2m −1
(B) 4m
(C) 5m
(D) m/5
(E) 6m/5
Rationale: 14m - n = p
Add n to both sides:
14m = n + p
Add m to both sides:
15m = n + p + m
Now, divide both sides by 3
5m = (n + p + m)/3 = the average of n, p, and m
C
Answer: (C) 5m
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
(A) 2 : 3
(B) 3 : 2
(C) 3 : 4
(D) 4 : 3
(E) 2 : 1
Rationale: Explanation:
Let the speed of the train be x km/hr and that of the car be y km/hr.
Then,	120/x+480/y=8 =>1/x+4/y=1/15....(i)
And, 200/x+400/y=25/3	=>1/x+2/y=1/24....(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
ANSWER IS C
Answer: (C) 3 : 4
Question: The average age of a husband and a wife is 23 years when they were married FOUR years ago but now the average age of the husband, wife and child is 19 years(the child was born during the interval). What is the present age of the child?
(A) 6
(B) 5
(C) 8
(D) 4
(E) 2
Rationale: 27 * 2 = 54
20 * 3 = 60
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6 years.Answer: A
Answer: (A) 6
Question: John and David work at a hospital with 10 other workers. For an internal review, 2 of the 10 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen?
(A) 1/45
(B) 1/35
(C) 1/25
(D) 1/15
(E) 1/10
Rationale: Probability that John and David will both be chosen out of 8 workers
= (2/10)*(1/9)
= 1/45
Answer A
Answer: (A) 1/45
Question: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Soln:
Given that x is positive and single digit and based on 4/3*x being one of them,
Assume x as 3
this gives the list as 4, 6, 3, 5, 7
when ordered, 3,4,5,6,7
hence median is 5
Answer is C
Answer: (C) 5
Question: In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 95π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
(A) 190π
(B) 210π
(C) 240π
(D) 320π
(E) 380π
Rationale: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.
4(95π) = 380π
The answer is E.
Answer: (E) 380π
Question: If a < b < c , which of the following must be true?
(I) a^2 < b^2
(II) b − a < c
(III) a^2 < b^2 < c^2
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III
Rationale: (I) a^2 < b^2. Not necessarily true fractions: try a=0.1 and b=0.2.
(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: A.
Answer: (A) None
Question: A bag contains 23 purple jellybeans, 12 green jellybeans, and 15 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
(A) 15%
(B) 20%
(C) 24%
(D) 30%
(E) 35%
Rationale: p = 23 , g=12 , y=15
total = 50
p(green)=(12/50)*100 = 24% . Ans = C
Answer: (C) 24%