mathewhe/aqua_rat huggingface dataset:
Question: Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail?
(A) 3/4
(B) 1/4
(C) 3/8
(D) 1/2
(E) 1/8
Rationale: Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting 3 heads
Then E = {HHH,HTH,THH,HHT}
P(E) = n(E)/n(S) =4/8 = 1/2
Answer is D
Answer: (D) 1/2
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
(A) 9
(B) 9.6
(C) 10
(D) 10.8
(E) 7
Rationale: Explanation:
Relative speed = (60 + 40) km/hr =[ 100 x ( 5 / 18 ) ]m/sec = ( 250 /9 ) m/sec.
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = [ 300 x ( 9/250 ) ] sec = ( 54/ 5 )sec = 10.8 sec. Answer: D
Answer: (D) 10.8
Question: An eccentric casino owner decides that his casino should only use chips in $5 and $9 denominations. Which of the following amount cannot be paid out using these chips?
(A) $31
(B) $37
(C) $33
(D) $24
(E) $15
Rationale: Yes, the number of 5 or/and 9 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.
Each option but A can be represented as the sum of a multiple of 5 and a multiple of 9:
A. $33 = 5*3 + 9*2
B. $37 = 5*2 + 9*3
C. $24 = 5*3 + 9*1
E. $15 = 5*3
Answer: A.
Answer: (A) $31
Question: The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions ? (use π = 22⁄7)
(A) 40 m2
(B) 44 m2
(C) 48 m2
(D) 36 m2
(E) None of these
Rationale: Required area covered in 5 revolutions
= 5 × 2πrh = 5 × 2 × 22⁄7 × 0.7 × 2 = 44 m2
Answer B
Answer: (B) 44 m2
Question: The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.
(A) 100m
(B) 125m
(C) 150m
(D) 278m
(E) 300m
Rationale: Sol. Area of the field = Total cost/rate = (333.18/25.6)hectares = 13.5 hectares
(13.5 x 10000) m^2 = 135000 m^2.
Let altitude = x metres and base = 3x metres.
Then, (1/2)* 3x* x = 135000 <=>x^2= 90000 <=>x = 300.
Base = 900 m and Altitude = 300 m.
Ans: E
Answer: (E) 300m
Question: A chemist mixes one liter of pure water with x liters of a 75% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
(E) 3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 75%
Concentration of salt in the mixed solution = 15%
The pure solution and the salt solution is mixed in the ratio of --> (75 - 15)/(15 - 0) = 4/1
1/x = 4/1
x = 1/4
Answer: A
Answer: (A) 1/4
Question: Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 22 square meters. What is the area that is covered with three layers of rug ?
(A) 18 square meters
(B) 20 square meters
(C) 24 square meters
(D) 19 square meters
(E) 30 square meters
Rationale: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}
140 = 200 - 22 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 19.
Answer: D.
Answer: (D) 19 square meters
Question: A thief is noticed by a policeman from a distance of 450 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?
(A) 50 meter
(B) 100 meter
(C) 220 meter
(D) 120 meter
(E) 350 meter
Rationale: Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes =
1/60∗6=1/10=100meters
So distance between them after 6 minutes = 450 - 100
= 350 meters
Option E
Answer: (E) 350 meter
Question: How many bricks, each measuring 80 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
(A) 6400
(B) 2000
(C) 5500
(D) 7400
(E) 3000
Rationale: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (80 x 11.25 x 6) = 2000
ANSWER:B
Answer: (B) 2000
Question: A scale 6 ft. 8 inches long is divided into 4 equal parts. Find the length of each part.
(A) 20 inches
(B) 77 inches
(C) 66 inches
(D) 97 inches
(E) 66 inches
Rationale: Explanation:
Total length of scale in inches = (6*12) + 8 = 80 inches
Length of each of the 4 parts = 80/4 = 20 inches
ANSWER:A
Answer: (A) 20 inches
Question: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 14 multiples of 14, how many multiples of 7 are there in Q?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 14+13 = 27.
The answer is B.
Answer: (B) 27
Question: What will be the difference in simple and compound interest on 4000 after three years at the rate of 10 percent per annum?
(A) 160
(B) 42
(C) 62
(D) 124
(E) None of these
Rationale: For 3 years:
Diff.=Sum×(rate)2(300+rate)/(100)3
= 4000×10×10×310/100×100×100 = 124
Answer D
Answer: (D) 124
Question: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 16 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
(A) 6 2/3
(B) 15
(C) 20
(D) 25
(E) 26 2/3
Rationale: Here is how I did it:
The cyclist travels 16 miles in 60 mins, so in 5 mins he will travel [(16*5)/60] miles, which equals 4/3 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 4/3 miles, he will take [(60*4/3)/4] = 20 mins.
hence 20-5=15 mins
B
Answer: (B) 15
Question: The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is?
(A) 551 cm
(B) 151 cm
(C) 156 cm
(D) 165 cm
(E) 146 cm
Rationale: Total height
= 150 * 50 = 7500 cm.
New average
= [7500 - 5 * 146 + 5 * 156 ] / 50
= 151 cm.
Answer: B
Answer: (B) 151 cm
Question: Excluding stoppages, the speed of a train is 60 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Explanation:
T = 20/60 * 60 = 20
Answer: Option E
Answer: (E) 20
Question: A man can do a piece of work in 10days, but with the help of his son, he can finish it in 5days. In what time can the son do it alone?
(A) 5
(B) 8
(C) 7
(D) 10
(E) 15
Rationale: Son's 1day work = 1/5 - 1/10 = 1/10
Son alone can do the work in 10days
Answer is D
Answer: (D) 10
Question: Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length Q of time will elapse before they chime together again?
(A) 2 hr. and 24 min.
(B) 4 hr. and 48 min.
(C) 1 hr. and 36 min.
(D) 5 hr.
(E) 2 hr.
Rationale: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.
So the LCM of the three time intervals (18, 24,32) would be the answer.
LCM (18, 24, 32) Q= 288 => 4 hours 48 mins.B
Answer: (B) 4 hr. and 48 min.
Question: Marks of a student were wrongly entered in computer as 83, actual marks of that student were 63. Due to this mistake average marks of whole class got increased by half (1/2). Find the total number of students in that class.
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: Explanation:
Suppose total number of students are = X
Totalincrease=x∗1/2=x/2
=>x/2=83−63=20
=>x=40
Answer: Option D
Answer: (D) 40
Question: A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 62. If the marks secured by Reema was written as 50 instead of 85 then find the correct average marks up to two decimal places.
(A) 63
(B) 74.31
(C) 72.43
(D) 73.43
(E) Cannot be determined
Rationale: Total marks = 35 x 62 =2170
Corrected total marks = 2170 - 50 + 85 =2205
Correct Average = 2205/35 = 63
Answer : A
Answer: (A) 63
Question: Find the largest number that will divide 43,91,183 so as to leave the same reminder in each case.
(A) 5
(B) 4
(C) 26
(D) 35
(E) 9
Rationale: Explanation:
Required Number=H.C.F of(91-43),(183-91) and (183-43)
H.C.F of 48,92 and 140=4
Answer:B
Answer: (B) 4
Question: Marla is hanging a banner diagonally across a rectangular room. The length of the room is 2 feet shorter than its width. If the total area of the room is 120 square feet, what is the length of the banner (in feet)?
(A) Between 13 and 14
(B) Between 14 and 15
(C) Between 15 and 16
(D) Between 16 and 17
(E) Between 17 and 18
Rationale: To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have
x(x - 2) = 120. By putting the equation in standard form, we get x^2-2x-120=0. By using the quadratic formula, we get roots of -10 and 12. We know that x is the width, and x-2 is the length, so by using the roots, we get 12 as the width (x), and 10 as the length (x-2).
Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=12^2+10^2
=144+100
=244
The square root of 244 is less than 16, since 16^2 = 256. Going down a number, we can compute 15^2 = 225 < 224. Therefore, the length of the diagonal must be between 15 and 16.
The correct answer is C.
Answer: (C) Between 15 and 16
Question: A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 10 km per hour and the level part at the rate of 15 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 15 km per hour for the entire route?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: Let V be the speed on the downhill section.
Let D be the distance of each of the three equal sections.
Total time T = T1+T2+T3 and 3D/T = 15 km/hour
3D / (D/10 + D/15 + D/V) = 15
1/5 = 1/10 + 1/15 + 1/V
1/V = 1/30 and so V = 30 km/h
The answer is C.
Answer: (C) 30
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 9),
what is the maximum possible area of C?
(A)  6
(B)  9
(C)  24
(D)  32
(E)  64
Rationale: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
C
Answer: (C)  24
Question: If a certain sample of data has a mean of 24.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 16.5
Rationale: The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is E.
Answer: (E) 16.5
Question: A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 25 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
(A) 5:00
(B) 5:34
(C) 5:42
(D) 6:00
(E) 6:24
Rationale: C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15 = 45 minutes have passed.
C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60 = 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.
C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.
C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of 4/3 * 2/3 * 5/4 * 45 = 50 minutes.
C4 loses 10 minutes every hour.
In 6 hours, C4 will lose 6*10 = 60 minutes = 1 hour.
Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 5:42pm.
The correct answer is C.
Answer: (C) 5:42
Question: If HCF of two numbers is 11 and the product of these numbers is 363, what is the the greater number?
(A) 33
(B) 36
(C) 38
(D) 42
(E) 44
Rationale: Let the numbers be 11a and 11b
11a × 11b = 363
=> ab = 3
co-primes with product 3 are (1, 3)
Hence the numbers with HCF 11 and product 363
= (11 × 1, 11 × 3)
= (11, 33)
Hence, numbers are 11 and 33
The greater number =
A)
Answer: (A) 33
Question: A man can row with a speed of 10 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is?
(A) 10 kmph
(B) 5 kmph
(C) 40 kmph
(D) 22 kmph
(E) 25 kmph
Rationale: M = 10
S = 30
DS = 10 + 30 = 40
ANSWER:C
Answer: (C) 40 kmph
Question: Find the ones digit of 73^356
(A) 1
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: The units digit of 73^356 will be the same as the units digit of 3^356.
3^1=3 --> the units digit is 3;
3^2=9 --> the units digit is 9;
3^3=27 --> the units digit is 7;
3^4=81 --> the units digit is 1;
3^5=243 --> the units digit is 3 AGAIN;
...
So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 356=356+0=(multiple of 4)+0, then the units digit of 3^356 will be thus 1.
Answer: A.
Answer: (A) 1
Question: 10^25 - 250 is divisible by all of the following except:
(A) A.11
(B) B.15
(C) C.5
(D) D.6
(E) E.3
Rationale: The last three digits ( 1000 - 250 ) 750
750 is divisible by 15,3,6,5
750 is not evenly divisible by 11 so the answer is A) 11
Answer: (A) A.11
Question: If A speaks the truth 85% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
(A) 0.49
(B) 0.48
(C) 0.41
(D) 0.482
(E) 0.51
Rationale: Explanation:
Probability that A speaks truth is 85/100 = 0.85
Probability that B speaks truth is 60/100 = 0.6
Since both A and B are independent of each other
So probability of A intersection B is P(A) × P(B) =0.85 × 0.6 = 0.51
Answer: E
Answer: (E) 0.51
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
(A) 600 m
(B) 300 m
(C) 400 m
(D) 700 m
(E) 500 m
Rationale: A
600 m
Distance covered by Amar = 18/4.8 (1.6km) = 3/8(1600) = 600 m
Answer: (A) 600 m
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years?
(A) Rs.3129
(B) Rs.3120
(C) Rs.3108
(D) Rs.3106
(E) Rs.3127
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 =
Rs.3120
Answer:B
Answer: (B) Rs.3120
Question: A person travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47 minutes. Find the total distane
(A) 3 km
(B) 4 km
(C) 6 km
(D) 9 km
(E) 5 km
Rationale: Explanation:
Let the distance be 3x km,
then,
x/3+x/4+x/5=47/60
47x /60= 47 /60
x=1
So total distance = 3*1 = 3 Km
Option A
Answer: (A) 3 km
Question: An item is being sold for $10 each. However, if a customer will “buy at least 3” they have a promo discount of 32%. Also, if a customer will “buy at least 10” items they will deduct an additional 8% to their “buy at least 3” promo price. If Sam buys 10 pcs of that item how much should he pay?
(A) $92.00
(B) $88.00
(C) $87.04
(D) $80.96
(E) $70.00
Rationale: Without any discount Sam should pay 10*10=$100. Now, the overall discount would be slightly less than 40%, thus he must pay slightly more than $60. Only answer choice E fits.
Answer: E.
Answer: (E) $70.00
Question: A can run 4 times as fast as B and gives B a start of 66 m. How long should the race course be so that A and B might reach in the same time?
(A) 88 m
(B) 60 m
(C) 80 m
(D) 65 m
(E) 75 m
Rationale: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 66m he gains 66*(4/3)
I.e 88m
ANSWER:A
Answer: (A) 88 m
Question: The length of a side of a hexagon is 8 inches. What is the perimeter?
(A) 40
(B) 44
(C) 48
(D) 50
(E) 38
Rationale: Hexagon. It means 6 equal sides.
p = 6(8) = 48 inches
Answer C
Answer: (C) 48
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 12 sec, then the speed of each train is?
(A) 22
(B) 77
(C) 36
(D) 90
(E) 21
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (300 + 300)/12 => x = 25
Speed of each train = 10 m/sec.
= 25 * 18/5 =- 90 km/hr.
Answer: D
Answer: (D) 90
Question: Ms. Lopez deposits $ 150 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
(A) $118.00
(B) $120.00
(C) $181.15
(D) $122.00
(E) $140.00
Rationale: Using Formula - A = P(1+r/n)^nt
Given
P=150
n=2
t=1
r=0.2
Substituting value in formula
A = 150(1+0.2/2)^2
A= 181.15$=C
Answer: (C) $181.15
Question: How many four digit numbers divisible by 4 can be made with digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: A number is divisible by 4 if the last 2 numbers are divisible by 4 (divisible by 2 twice)
Ending can be
12
24
32
42
52
Case: Ending with 12,24,32,42,54
First digit - 3 choices
Second digit - 2 choices
Third digit - 1 choice
Fourth digit - 1 choice
6 possible choices for each ending (e.g. 3412,3512, 3212 ,4512 ,5312 ,5412)
Total number of 4 digit numbers divisible by 4 = 6 * 5 = 30
ANSWER:C
Answer: (C) 30
Question: A candidate appearing for an examination has to secure 42% marks to pass paper I. But he secured only 60 marks and failed by 20 marks. What is the maximum mark for paper I?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 190
Rationale: he secured 60 marks nd fail by 20 marks so
total marks for pass the examinatn=80
let toal marks x
x*42/100=80
x=190
ANSWER:E
Answer: (E) 190
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 67 kmph
(C) 15 kmph
(D) 88 kmph
(E) 12 kmph
Rationale: Speed of the boat in still water
= (60+90)/2
= 75 kmph. Speed of the stream
= (90-60)/2
= 15 kmph.
Answer:C
Answer: (C) 15 kmph
Question: By selling a watch for Rs.800/-, a man loses 20% what is that watch cost price
(A) s. 700/-
(B) s. 800/-
(C) s. 880/-
(D) s. 900/-
(E) s. 1000/-
Rationale: 80 % ------> 800 (80 * 10 = 640)
100 % ------>1000 (100 * 10 = 1000)
Cost price = Rs. 1000/-
E
Answer: (E) s. 1000/-
Question: If 100!/30^n is an integer, which of the following is the greatest possible value of n?
(A) 28
(B) 24
(C) 20
(D) 15
(E) 10
Rationale: 30^n = 2^n * 3^n * 5^n
100! has 97 2's, 48 3's and 24 5's
Since each of 2, 3 and 5 is required to form 30 and there are only 24 5's there can only be 24 30's in 100!
Answer: B
Answer: (B) 24
Question: Find the average of all numbers between 6 and 36 which are divisible by 7
(A) 20
(B) 15
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
Average=(7+14+21+28+35)/7=105 / 7=15
Option B
Answer: (B) 15
Question: A batch of widgets costs p + 8 dollars for a company to produce and each batch sells for p(7 – p) dollars. For which of the following values of p does the company make a profit?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: to make profit, selling price should be greater than cost price
p(7-p) - p-8 >0
=> p^2-6*p+8<0
hence p=3
A
Answer: (A) 3
Question: Find large number from below question The difference of two numbers is 2500. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 3345
(B) 1250
(C) 1540
(D) 2997
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 2500= 6x + 15
5x = 2485
x = 497
Large number = 497+1365 = 2997
D
Answer: (D) 2997
Question: A walks at 30 kmph and 30 hours after his start, B cycles after him at 42 kmph. How far from the start does B catch up with A?
(A) 1200km
(B) 1500km
(C) 2000km
(D) 2500km
(E) 3150km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 30 hours.
x/30 - x/42 = 30
x = 3150 km
Answer is E
Answer: (E) 3150km
Question: The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Speed of the boat downstream = 90 + 18 = 108 kmph
= 108 * 5/18 = 30 m/s
Hence time taken to cover 330 m = 330/30 = 11 seconds.
Answer: A
Answer: (A) 11
Question: If p/q =4/5, then the value of 11/7 + {(2q - p) / (2q + p)} is ?
(A) 3 / 7
(B) 34
(C) 1
(D) 2
(E) 3
Rationale: Answer
Given Exp. = 11 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 11/7 + {2-p/q) / (2 + p/q)}
= 11/7 + {(2 - 4/5) / (2 + 4/5)}
= 11/7 + 6/14
= 11/7 + 3/7
=14/7
=2
Correct Option: D
Answer: (D) 2
Question: Two cubes of their volumes in the ratio 27 : 125. The ratio of their surface area is:
(A) 1.5:5
(B) 2:5
(C) 3:5
(D) 1:5
(E) 4:5
Rationale: The ratio of their surface area is
27 : 125
3 : 5
Answer is C.
Answer: (C) 3:5
Question: At a certain supplier, a machine of type A costs $21,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $10,560
(B) $11,200
(C) $12,000
(D) $12,800
(E) $13,200
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 42000 + (42000 - 20% of 42000) + 40% of (42000 - 20% of 42000)
= 55440
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 55440 = 10560
Hence, A.
Answer: (A) $10,560
Question: A lends Rs. 1500 to B and a certain sum to C at the same time at 8% per annum simple interest. If after 4 years, A altogether receives Rs. 1400 as interest from B and C, then the sum lent to C is
(A) Rs.2875
(B) Rs.1885
(C) Rs.2245
(D) Rs.2445
(E) Rs.2615
Rationale: Explanation :
Let the sum lent to C be Rs. x
Simple Interest for Rs.1500 at 8% per annum for 4 years
+ Simple Interest for Rs.x at 8% per annum for 4 years = Rs.1400
⇒1500×8×4/100+ x × 8×4/100=1400
⇒480+32x/100=1400
⇒32x/100=920
⇒x=920×100/32=2875
Answer : Option A
Answer: (A) Rs.2875