mathewhe/aqua_rat huggingface dataset:
Question: A can do a piece of work in 4 days. B can do it in 15 days. With the assistance of C they completed the work in 24 days. Find in how many days can C alone do it?
(A) 0.391 days
(B) 0.491 days
(C) 0.331 days
(D) 1.391 days
(E) 0.301 days
Rationale: C = 1/2 - 1/24 - 1/15 = 0.391 days
ANSWER:A
Answer: (A) 0.391 days
Question: what is the compound interest on rs:70,000 for 4 months at the rate of 5% per annum
(A) 1171.98
(B) 1172.98
(C) 1173.98
(D) 1174.98
(E) 1175.98
Rationale: it is monthly compound
rate=5/12% per month
70000*(1+5/1200)^4-70000=1173.98
ANSWER:C
Answer: (C) 1173.98
Question: A bus trip of 660 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: The time is the distance/speed. The time difference is 1 hour.
660/V - 660/(V+5) = 1
660(V+5) - 660V = (V)(V+5)
3300 = (V)(V+5)
55*60 = (V)(V+5)
V = 55 mph
The answer is D.
Answer: (D) 55
Question: A worker's daily wage is increased by 50% and the new wage is $51 per day. What was the worker's daily wage before the increase?
(A) $28
(B) $32
(C) $34
(D) $35
(E) $40
Rationale: Let x be the daily wage before the increase.
1.5x = $51
x = $34
The answer is C.
Answer: (C) $34
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 5578
(B) 5552
(C) 5550
(D) 5528
(E) 5598
Rationale: Total production of salt by the company in that year
= 5000 + 5100 + 5200 + .... + 6100
= 66600.
Average monthly production of salt for that year
= 66600/12 = 5550.
Answer:C
Answer: (C) 5550
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 70 ps per meter is?
(A) 287
(B) 369
(C) 175
(D) 279
(E) 361
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 0.70
= Rs.175
Answer:C
Answer: (C) 175
Question: The average of five integers is 56, and none of these integers is greater than 100. If the average of three of the integers is 59, what is the least possible value of one of the other two integers?
(A) 3
(B) 15
(C) 20
(D) 21
(E) 30
Rationale: When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 56
So, the sum of ALL 5 integers = (56)(5) =280
The average of three of the integers is 65
So, the sum of the 3 integers = (59)(3) =177
So, the sum of the 2 REMAINING integers =280-177=103
If the sum of the 2 REMAINING integers =103, and we want to minimize one value, we must MAXIMIZE the other value.
100 is the maximum value so let 1 integer = 100, which means the other must equal 3
Answer: A
Answer: (A) 3
Question: The average (arithmetic mean) of seven numbers is 7. If 4 is subtracted from each of three of the numbers, what is the new average?
(A) 4.2
(B) 6.3
(C) 5.2
(D) 7.9
(E) 8.3
Rationale: Sum of 7 numbers = 7*7=49
If4 is subtracted from each of three of the numbers , we subtract 4*3=12 from the total sum
Sum of 7 number after subtracting 4 from each of three of the numbers =49-12=37
New average = 37/7=5.2
Answer C
Answer: (C) 5.2
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?
(A) p
(B) 2p
(C) 5p
(D) 7p
(E) p^2
Rationale: Y=30p
other number is 14p
then GCF(30p,14P)=2P; B is the correct answer
Answer: (B) 2p
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 72
(B) 67
(C) 108
(D) 26
(E) 27
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
Answer:C
Answer: (C) 108
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 60 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
(A) 8 km/hr.
(B) 32 km/hr.
(C) 34 km/hr.
(D) 18 km/hr.
(E) 12 km/hr.
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (60 + 60)/12
2x = 10
x = 5.
Speed of each train = 5 m/sec = 5 x 18/5 km/hr = 18 km/hr.
answer :D
Answer: (D) 18 km/hr.
Question: Find the value for m?
21(m + n) + 21 = 21(-m + n) + 21
(A) 0
(B) -1
(C) 1
(D) 2
(E) 3
Rationale: 21m + 21n - 21 = -21m + 21n + 21
42m= 42 => m = 1
C
Answer: (C) 1
Question: Excluding the stoppages, the speed of a bus is 48 km/hr and including the stoppages the speed of the bus is 12 km/hr. For how many minutes does the bus stop per hour?
(A) 45 min
(B) 10 min
(C) 12 min
(D) 20 min
(E) 18 min
Rationale: Speed of the bus without stoppage=48 km/hr
Speed of the bus with stoppage=12 km/hr
Difference in speed=36 km/hr
so,the time taken in the stoppages = time taken to cover 36 km=(36/48)hr = 3/4 hr =45 min
ANSWER:A
Answer: (A) 45 min
Question: rahul played weel in this season.his current batting averagge is 50.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.
(A) 8
(B) 10
(C) 9
(D) 6
(E) 5
Rationale: 50x+78=54(x+1)
=>4x=24
=>x=6
ANSWER:D
Answer: (D) 6
Question: If 4x - y = 32 and −x + 2y = 5, then what is the value of 3x + y?
(A) 37
(B) 3
(C) 15
(D) 52/7
(E) 60/7
Rationale: 4x - y = 32
−x + 2y = 5
Adding both the equations --> 3x + y = 37
Answer: A
Answer: (A) 37
Question: Evaluate 2+22+222+2.22
(A) 269.72
(B) 268.22
(C) 248.21
(D) 248.22
(E) 268.21
Rationale: 2+22+222+2.22=248.22
Option D
Answer: (D) 248.22
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 7 sec
(B) 8 sec
(C) 9 sec
(D) 6 sec
(E) 1 sec
Rationale: T = 60/36 * 18/5
= 6 sec
Answer: D
Answer: (D) 6 sec
Question: S = { 1,5,3,7}
T = { 4,5,6,7 }
what is the probability that x chosen from S and y chosen from T will result x*y = even
(A) 1/3
(B) 4/5
(C) 2/3
(D) 1/2
(E) 1/6
Rationale: p: the probability that x*y is even, then p=1-p(x*y is odd)
p(x*y odd)=p(x odd)*p(y odd)=4/4*2/4=2/4
And p=1-2/4=1/2
Option: D
Answer: (D) 1/2
Question: P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 18
Rationale: Let work done by P in 1 day = p
work done by Q in 1 day =q
Work done by R in 1 day = r
p + q = 1/8 ---(1)
q + r= 1/12 ---(2)
p+ q+ r = 1/6 ---(3)
(3) – (2) => p = 1/6 - 1/12 = 1/12
(3) – (1) => r = 1/6 – 1/8 = 1/24
p + r = 1/12 + 1/24 = 3/24 = 1/8
=> P and R will finish the work in 8 days
Answer is B.
Answer: (B) 8
Question: In how many different ways can the letters of the word 'APPLE' be arranged?
(A) 10 ways
(B) 20 ways
(C) 30 ways
(D) 60 ways
(E) 40 ways
Rationale: Totally there are 5 letters on the word APPLE. it contains 1A,2P,1L,1E.
The no of ways is 5!/2!=120/2=60 ways.
ANSWER:D
Answer: (D) 60 ways
Question: A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on
bicycle at 9 km/hr. What is the distance travelled on foot?
(A) 16 km
(B) 14 km
(C) 12 km
(D) 10 km
(E) None of these
Rationale: Explanation:
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr
Distance = Speed * Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4
So distance traveled on foot = 4(4) = 16 km
Answer: Option A
Answer: (A) 16 km
Question: 15, 31, 63, 127, 255, ?
(A) 543
(B) 447
(C) 972
(D) 532
(E) 511
Rationale: E
511
Each number is double of the preceding one plus 1.
Answer: (E) 511
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
(A) 9
(B) 12
(C) 15
(D) 17
(E) 19
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Answer: (B) 12
Question: What is the area of a square field whose diagonal of length 24 m?
(A) 240 sq m
(B) 250 sq m
(C) 200 sq m
(D) 400 sq m
(E) 800 sq m
Rationale: d2/2 = (24 * 24)/2 = 240
ANSWER:A
Answer: (A) 240 sq m
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 14, 2
(B) 16, 4
(C) 14, 8
(D) 14, 4
(E) 14, 1
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14,y = 4.
Answer: D
Answer: (D) 14, 4
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 6
(B) 8
(C) 5
(D) 3
(E) 9
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h
= 9 cm
Answer:E
Answer: (E) 9
Question: A train 140 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
(A) 54 kmph
(B) 60 kmph
(C) 66 kmph
(D) 72 kmph
(E) 78 kmph
Rationale: speed of train relative to man: 140/6 * 18/5 km/hr
= 84 km/hr
let speed of train= x
therefore x+6 = 84
x= 84-6
x=78 km/hr
ANSWER:E
Answer: (E) 78 kmph
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.756 find the share of A.
(A) 240
(B) 388
(C) 288
(D) 277
(E) 122
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 756 = 288
Answer: C
Answer: (C) 288
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 6 ounces of corn syrup, how many ounces of water does it contain?
(A) 15
(B) 30
(C) 45
(D) 60
(E) 90
Rationale: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 6.
So, x = 195 / 2 ounces.
Water = (60 / 65) * (195 / 2) = 60 * 3 / 4 = 90 ounces.
Ans E
Answer: (E) 90
Question: If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
(A) 141
(B) 200
(C) 412
(D) 391
(E) 612
Rationale: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...
A + (A+2) + (A+4) = 3A + 6
We know that 3A + 6 COULD equal one of those five answers; we just have to find it...
Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer
Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer
Could 3A + 6 = 412
3A = 406
A = 135.3333
This is NOT an EVEN INTEGER, so 412 is NOT the answer
Could 3A + 6 = 612
3A = 606
A = 202
This IS an EVEN INTEGER! The numbers would be 202, 204 and 206. This IS the answer
Final Answer:
E
Answer: (E) 612
Question: If |5x-10| = 100, then find the sum of the values of x?
(A) 1
(B) -2
(C) 3
(D) -3
(E) 4
Rationale: |5x-10| = 100
5x-10 = 100 or 5x-10 = -100
5x = 110 or 5x = -90
x = 22 or x = -18
sum = 21-18 = 3
Answer is C
Answer: (C) 3
Question: What is the are of an equilateral triangle of side 16 cm?
(A) 64√6
(B) 64√9
(C) 64√4
(D) 64√3
(E) 64√2
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;
Answer: D
Answer: (D) 64√3
Question: Four packages have an average weight of 11.5 pounds. What is the minimum possible weight of the heaviest package in pounds if the median is 10 pounds?
(A) 11
(B) 11.5
(C) 13
(D) 15
(E) 16
Rationale: Let us denote the weights of the packages in pounds by a, b, c, d naming from the lightest one to the heaviest one. The median is 10 pounds. Therefore (b + c) / 2 = 10.
b + c = 20
The average is 11.5 pounds. Therefore (a + b + c + d) / 4 = 11.5.
a + (b + c) + d = 46
a + 20 + d = 46
a + d = 26
The weight a must be no greater than 10, since 10 is the median. Therefore the minimum possible weight of the heaviest package is 26 – 10 = 16 pounds (all the other packages would weigh 10 pounds in this case).
Answer: E
Answer: (E) 16
Question: If log(2a - 3b) = log a - log b, then a =
(A) 3b2/2b -1
(B) 3b/2b -1
(C) b2/2b + 1
(D) 3b2/2b + 1
(E) None of these
Rationale: 2a- 3b = a/b
=>2ab - 3b2 = a
=>3b2 = a(2b - 1)
Therefore, a = 3b2/2b -1.
ANSWER:A
Answer: (A) 3b2/2b -1
Question: A and B start a business with Rs.5000 and Rs.7000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:5
(B) 5:7
(C) 3:9
(D) 5:3
(E) 3:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
5000 : 7000 => 5:7,Answer: B
Answer: (B) 5:7
Question: How many different three-digit multiples of 5 can be composed of digits 2, 3, 4, and 5 if none of the digits is repeated?
(A) 3
(B) 6
(C) 10
(D) 12
(E) 18
Rationale: Available: 2, 3, 4, 5
You need to make 3 digit numbers which are multiples of 5.
___ ___ ___
For the number to be a multiple of 5, it must end with either 0 or 5. We only have 5 available so the number must end with 5.
___ ___ 5
Now you select 2 numbers out of the leftover 3 numbers (2, 3 and 4) in 3C2 ways and arrange them in the 2 places in 2! ways which gives you 3C2*2! = 6
or you can say that you can select a number for the hundreds place in 3 ways and select a number for the tens place in 2 ways (since numbers cannot be repeated). So you can make the number in 3*2 = 6 ways
ANS:B
Answer: (B) 6
Question: Which of the following is the lowest positive integer that is divisible by 7, 8, 9, 10, and 11?
(A) 27,720
(B) 29,940
(C) 31,960
(D) 33,970
(E) 35,890
Rationale: The number needs to be divisible by 7, 2^3, 3^2, 2*5, and 11.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 * 11 = 27,720
The answer is A.
Answer: (A) 27,720
Question: A sum of money lent out at S.I. amounts to a total of $420 after 2 years and to $595 after a further period of 5 years. What was the initial sum of money that was invested?
(A) $310
(B) $320
(C) $330
(D) $340
(E) $350
Rationale: S.I for 5 years = $595 - $420 = $175
The S.I. is $35/year
S.I. for 2 years = $70
Principal = $420 - $70 = $350
The answer is E.
Answer: (E) $350
Question: 5/9 of the part of the population in a villagae are males.if 30 % of the males are married.the percentage of unmarried females in the total population is..
(A) 250/9%
(B) 150/9%
(C) 350/9%
(D) 450/9%
(E) 550/9%
Rationale: Let total population = p
no. of males =5p/9
no. of females =(p-5p/9)=4p/9
married males = 30% of 5p/9=30*5p/100*9 =p/6
married females = p/6
unmarried females =(4p/9-p/6)=5p/18
%age of unmarried females in the total population = {(5p/18)/p}*100= 250/9%
ANSWER:A
Answer: (A) 250/9%
Question: Find the value of (50+ 20/90) × 90
(A) 2520
(B) 3520
(C) 4520
(D) 1520
(E) 1750
Rationale: (4500+20)/90*90 = 4520
Answer : C
Answer: (C) 4520
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 338
(B) 378
(C) 200
(D) 298
(E) 122
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.
Answer: C
Answer: (C) 200
Question: A can complete a project in 30 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: A's 1day work=1/30;
B's 1day work=1/30;
(A+B) 1day work=(1/30+1/30)=1/15;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 1/15 work in 1 day...
They did 2/3 w in 10 days.
Total days=(10+10) = 20
ANSWER:C
Answer: (C) 20
Question: If a sum of money doubles itself in 5 years at simple interest, the ratepercent per annum is
(A) 12
(B) 12.5
(C) 20
(D) 13.5
(E) 14
Rationale: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 5) = 20
Option C
Answer: (C) 20
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 8:30 a.m. and drives north on the same highway at an average speed of 55 km per hour. Mr. Dinkle will
(A) overtake Mr. Smitherly at 10:30 a.m.
(B) overtake Mr. Smitherly at 11:30 a.m.
(C) overtake Mr. Smitherly at 1:30 p.m.
(D) be 30 miles behind at 9:35 a.m.
(E) never overtake Mr. Smitherly
Rationale: After thirty minutes, Mr. Smitherly is ahead by 25 km.
Mr. Dinkle gains on Mr. Smitherly 5 km each hour.
5 hours after 8:30 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is C.
Answer: (C) overtake Mr. Smitherly at 1:30 p.m.
Question: A and B can do a piece of work in 12 days. With the help of C they finish the work in 3 days. C alone can do that piece of work in?
(A) 40 days
(B) 2 days
(C) 4 days
(D) 8 days
(E) 40 days
Rationale: C
30 days
C = 1/3 – 1/12 = 1/4 => 4 days
Answer: (C) 4 days
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
(A) 2C7 * 10C6
(B) 2C7 * 17C5
(C) 2C7 * 10C5
(D) 2C9 * 10C5
(E) 2C7 * 30C5
Rationale: Here, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected 10C5 ways. Hence the total number of different ways of selection = ¹²C₅ * ¹⁰C₅ = ¹²C₇ * ¹⁰C₅
= 12C5 = 12C7
Answer:C
Answer: (C) 2C7 * 10C5
Question: In a bag, there are 6 brown, 4 blue and 10 orange pens. One pen is picked up randomly. What is the probability that it is neither brown nor blue?
(A) 1/4
(B) 1/5
(C) 1/3
(D) 1/2
(E) 3/4
Rationale: Explanation :
Neither brown nor blue means the pen drawn is orange.
Total number of outcomes = (6+4+10) = 20.
Number of Favourable outcomes = 10 = Number of orange pens.
Hence, Probability of the event = 10/20 = 1/2.
Answer : D
Answer: (D) 1/2
Question: A and B are walking with 25 kmph and 30 kmph. A is walking towards east and B is towards south. They both started at 7:00 A.M at what time they are 130 metres apart.
(A) 130m
(B) 140m
(C) 150m
(D) 160m
(E) 170m
Rationale: let after t sec they are 130m apart then
(25* 5/18 *t)^2 + (30* 5/18 *t)^2 = 130^2
=> t * (5/18) * 5 * √ 61 = 130
=> t = 12.98425 sec ~ 13 sec
so, at 7:00:13 AM they are 130m apart.
ANSWER:A
Answer: (A) 130m
Question: Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest E?
(A)  60
(B)  61
(C)  62
(D)  63
(E)  64
Rationale: 60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=E
answer is A.
Answer: (A)  60
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.82. How much was lent at 5%?
(A) 899
(B) 866
(C) 878
(D) 800
(E) 877
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 82
5x/100 + 90 – 6x/100 = 82
x/100 = 8
=> x = 800
Answer:D
Answer: (D) 800
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
(A) 41
(B) 23
(C) 56
(D) 99
(E) 87
Rationale: Explanation:
30 * 33/2 = 5/2 * 2 * x => x = 99
Answer: D
Answer: (D) 99
Question: The sum of all the integers g such that -26 < g < 24 is
(A) 0
(B) -2
(C) -25
(D) -49
(E) -51
Rationale: Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 g= -49.
D is the answer.
Answer: (D) -49
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 18
(B) 99
(C) 77
(D) 62
(E) 12
Rationale: 8/12 + 6/x = 1
X = 18 days
Answer:A
Answer: (A) 18
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 57.5 m
(B) 127.5 m
(C) 150.7 m
(D) 98.6 m
(E) 95 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.
ANSWER:B
Answer: (B) 127.5 m
Question: The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?
(A) 1:4
(B) 1:16
(C) 1:8
(D) 1:64
(E) 2:3
Rationale: 4πr12 : 4πr22 = 1 : 4
r1 : r2 = 1 : 2
4/3 πr13 : 4/3 πr23
r13 : r23 = 1 : 8
ANSWER:C
Answer: (C) 1:8
Question: Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c =
(A) 18
(B) 15
(C) -13
(D) -21
(E) -24
Rationale: f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c =
f(4) = 0= 16+4b+c--- Taking 16 to the other side
-> 4b+c= -16
f(-3) = 0= 9-3b+c --- taking -3b+c to the other side
-> 3b-c=9
When we add these 2 equations, we get 7b= -7---> b= -1
And while substituting b= -1 we get c= -12.
b+c= -13--- Answer C
Answer: (C) -13
Question: An accurate clock show 8 o’ clock in the morning. The hour hand then rotates by 90o. The time in the clock is:
(A) 9 o’clock
(B) 10 o’ clock
(C) 11 o’clock
(D) 12 o’clock
(E) 8 o’clock
Rationale: as from 9 o clock to 12 o clock is 90 degrees so 8 is one less than nine and hence tha answer will be one less than 12 that is 11 o clock
ANSWER:C
Answer: (C) 11 o’clock
Question: If x is negative and y is positive, which of the following cannot be positive?
(A) xy
(B) -xy
(C) x/-y
(D) x^2/y
(E) x^4/y
Rationale: - * + = -
xy is not positive.
Answer : A
Answer: (A) xy
Question: Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1235
(B) 1345
(C) 1678
(D) 1767
(E) 1671
Rationale: Let the smaller number be x. Then larger number = (x + 1395).
x + 1395 = 6x + 15
5x = 1380
x = 276
Large number = 276+1395 = 1671
E
Answer: (E) 1671
Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $90 per day. What was his wage on the 8th day?
(A) $83
(B) $90
(C) $92
(D) $97
(E) $111
Rationale: Average daily wage of a worker for 15 consecutive working days = 90$
During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 90$
Wage on 8th day = 90*15 -( 87*7 + 90 *7)
= 1350 - (609 + 630)
=1350 - 1239
= 111
Answer E
Answer: (E) $111