mathewhe/aqua_rat huggingface dataset:
Question: A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
(A) $2,040
(B) $2,120
(C) $1,960
(D) $1,920
(E) $1,400
Rationale: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost.
Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $3,000-$880=$2,120.
Answer: B.
Answer: (B) $2,120
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be B's share of the earnings?
(A) $1100
(B) $520
(C) $780
(D) $1170
(E) $630
Rationale: Explanatory Answer
A, B and C will share the amount of $2340 in the ratio of the amounts of work done by them.
As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.
Similarly, B will complete 1/8th and C will complete 1/12th of the work.
So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12
Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.
We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.
i.e., the ratio in which A : B : C will share $2340 will be 4 : 3 : 2.
Hence, B's share will be 3*2340/9 = 780
correct choice is (C)
Answer: (C) $780
Question: The timing of a college is from 11 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
(A) 56 minutes
(B) 52 minutes
(C) 30 minutes
(D) 48 minutes
(E) 44 minutes
Rationale: Explanation:
Total time a student spends in college = 5 hours 20 minutes = 280 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (280 â€“ 20)/5
= 52 minutes
ANSWER B
Answer: (B) 52 minutes
Question: Two identical cubes if one of them is painted pink on its 4 side and blue on the remaining two side then how many faces painted pink to other cube so that probability of getting cube is 1/3 when we roll both the cube.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 0 faces should be painted pink i.e all faces blue
ANSWER:A
Answer: (A) 0
Question: if p/q=3/4
then3p+9q=?
(A) 25/4
(B) 25/2
(C) 20/4
(D) 45/4
(E) 25/3
Rationale: 3p+9q=?
Divided by q,
3(p/q)+9=x
3*(3/4)+9=45/4
ANSWER:D
Answer: (D) 45/4
Question: Find the altitude of a parallelogram whose are is
5400cm2 and the base is 45cm
(A) 80 cm
(B) 90 cm
(C) 100 cm
(D) 110 cm
(E) 120 cm
Rationale: area of parallelogram =base * hight then 5400 cm2=45cm*h
h=120 cm
ANSWER:E
Answer: (E) 120 cm
Question: In what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 8 sec
(B) 1 sec
(C) 9 sec
(D) 7 sec
(E) 2 sec
Rationale: T = 70/36 * 18/5
= 7 sec
Answer:D
Answer: (D) 7 sec
Question: 30 ladies and 60 gentlemen are present at a party. There are 23 couples among them. If a lady and a gentleman is selected at random, what is the probability that they will be a couple?
(A) 1/200
(B) 1/100
(C) 1/50
(D) 1/40
(E) 23/1800
Rationale: In how many ways we can select a woman and a man from 30 women and 60 men? In 30*60 = 1800 ways.
We have a total of 23 couples so, the probability of selecting a couple is 23/1800 = 23/1800.
Ans- E
Answer: (E) 23/1800
Question: Sonika bought a V.C.R. at the list price of 18,600. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.
(A) 20,088
(B) 19,780
(C) 19,680
(D) 19,380
(E) None of these
Rationale: Sol. List price of V.C.R. =18,600
Rate of sales tax = 8%
∴ Sales tax = 8% of 18,600
= 8⁄100 × 18600 = 1488
So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,600 + 1488
= 20,088. Answer A
Answer: (A) 20,088
Question: A number when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31
(A) 5
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: Explanation:
P ÷ 44 = 432
=> P = 432 * 44 = 19008
P / 31 = 19008 / 31 = 613, remainder = 5
Option A
Answer: (A) 5
Question: In a certain group of 13 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
(A) 198
(B) 154
(C) 202
(D) 201
(E) 200
Rationale: Case 1
1french 2either German or Spanish: 4C1 * 9C2 = 144
Case 2
2french 1either German or Spanish: 4C2 * 9C1 = 54
Case 3
3french 4C3 = 4
Answer is C
Answer: (C) 202
Question: Car A runs at the speed of 58km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
(A) 11 : 6
(B) 12 : 7
(C) 29 : 18
(D) 15 : 6
(E) 13 : 6
Rationale: Sol. Distance travelled by Car A = 58 Ã— 8 = 464 km
Distance travelled by Car B = 70 Ã— 4 = 280 km
Ratio = 464/280 = 29 : 18
C
Answer: (C) 29 : 18
Question: A rectangle has a perimeter of 176 inches. The length of the rectangle is 8 inches more than its width. What is the area of the rectangle?
(A) 1,408 square inches
(B) 1,920 square inches
(C) 1,936 square inches
(D) 2,304 square inches
(E) None of these
Rationale: Explanation:
We have: (l - b) = 8 and 2(l + b) = 176 or (l + b) = 88.
Solving the two equations, we get: l = 48 and b = 40.
Area = (l x b) = (48 x 40) in2 = 1920 in2.
Correct answer: B
Answer: (B) 1,920 square inches
Question: What number comes next?
582, 693, 715, 826, 937, ?
(A) 113
(B) 231
(C) 245
(D) 158
(E) 123
Rationale: D
158
The numbers 58269371 are being repeated in the same sequence.
Answer: (D) 158
Question: The sum of the digits of [(10^x)^y]-64=279. What is the value of xy ?
(A) 28
(B) 29
(C) 30
(D) 31
(E) 32
Rationale: 1000−64=936. Whatever XY is you finish with 36==>3+6=9
Therefore, 279−9=270 and 270/9=30
Now you add the last two digits (3 and 6)
Answer is 30+2=32
ANSWER:E
Answer: (E) 32
Question: In the junior basketball league there are 18 teams, 1/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad?
(A) 4.
(B) 6.
(C) 7.
(D) 8.
(E) 10.
Rationale: total teams =18
bad teams=(1/3)*18=6
rich teams=9
so maximum value that the both rich and bad can take will be 9. so E= 10 can not be that value.
ans E.
Answer: (E) 10.
Question: On a trip covering 400 km, a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip?
(A) 15.5
(B) 16.0
(C) 16.5
(D) 17.0
(E) 17.5
Rationale: time 1 = 100 / 20 = 5 hours
time 2 = 300 / 15 = 20 hours
total time = 25 hours
average speed = 400 / 25 = 16 km/hr
The answer is B.
Answer: (B) 16.0
Question: A and B are two partially filled buckets of water. If 2 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 2 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
(A) 11
(B) 13
(C) 17
(D) 21
(E) 22/5
Rationale: Let A contains A, B contains B liters
so, (A-2)/(B+2)= 1/3.......(1) OR 3A-6 =B+2 OR 3A-B =8
again, (B-2)/(A+2)= 1/2..(2) OR 2B-4 =A+2 OR 2B-A =6
from (1)(2) we find A= 22/5
ans: E
Answer: (E) 22/5
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, the how old is B?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 15 years
(E) 16 years
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 37
5x = 35
x = 7.
Hence, B's age = 2x = 14 years.
C)
Answer: (C) 14 years
Question: After spending 40 percent machinery, 25 percent in building , 15 percent in raw material and 5 percent on furniture . John had a balance of Rs.1305. Total money with him was?
(A) 6700
(B) 8700
(C) 9400
(D) 9800
(E) 8900
Rationale: [100 - (40+25+5+15)] % of x = 1305
\inline \Rightarrow 15% of x =1305
\inline \Rightarrow \frac{15}{100}\times x=1305
\inline \therefore x=\frac{1305\times 100}{15}=8700
B
Answer: (B) 8700
Question: In an exam 49% candidates failed in English and 36% failed in Hindi and 15% failed in both subjects. If the total number of candidates who passed in English alone is 630. What is the total number of candidates appeared in exam?
(A) 2000
(B) 3000
(C) 3500
(D) 3800
(E) 4000
Rationale: not fail in english =51%
not fail in hindi =64%
not fail in both =30 %(49+36-15)
pass in english only=51-30=21
21/100*x=630
x=3000
ANSWER:B
Answer: (B) 3000
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 120?
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 120
4n< 113
n < 28. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 48)
Combining the two
-1.5 < n<48.25
n = 1 to 28 (48 integers)
and n = -1 and 0
so 30 integers.
E is the answer
Answer: (E) 30
Question: Express a speed of 108 kmph in meters per second?
(A) 30 mps
(B) 76 mps
(C) 26 mps
(D) 97 mps
(E) 16 mps
Rationale: 108 * 5/18
= 30 mps
Answer:A
Answer: (A) 30 mps
Question: The average weight of a group of boys is 30 kg. After a boy of weight 33 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) A)4
(B) B)8
(C) C)6
(D) D)2
(E) E)1
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 33 kg joins the group, total weight of boys = 30x + 33
So 30x + 33 = 31(x + 1) = > x = 2.
Answer:D
Answer: (D) D)2
Question: if the list price of a book is reduced by Rs.5,then a person can buy 5 more books for Rs.300. The original cost of the book is
(A) Rs.15
(B) Rs.20
(C) Rs.25
(D) Rs.30
(E) Rs.35
Rationale: 300/(x-5)-300/x=5
x=20
ANSWER:B
Answer: (B) Rs.20
Question: 5 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
(A) 30
(B) 21
(C) 10
(D) 15
(E) 12
Rationale: the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 5(5-1)/2 = 5*4/2 = 20/2 = 10
=> the answer is C(10)
Answer: (C) 10
Question: In a colony the municipality decided to number the houses and the shops. They want to number the shops with the numbers containing 3 between 1-100. The houses are 10-20 floored and at the back of the houses 8 feet is left for fire exit. How many shops can be numbered?
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: 3numbers containing 3
--->3,13,23,... = 10 numbers
---->30,31,32... = 10 numbers
total = 20 -1 = 19
ANSWER:A
Answer: (A) 19
Question: For which of the following does f(u)−f(v)=f(u−v) for all values of u and v?
(A) f(a)=a^2
(B) f(a)=a/2
(C) f(a)=a+5
(D) f(a)=2a−1
(E) f(a)=|a|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(u) = u^2 and f(v) = v^2
so L.H.S = u^2 - v^2
and R.H.S = (u-v)^2 ==> u^2 + v^2 -2uv.
so L.H.S not equal to R.H.S
with option 2. f(u) = u/2 and f(v) = v/2
L.H.S = u/2 - v/2 ==> 1/2(u-v)
R.H.S = (u-v)/2
so L.H.S = R.H.S which is the correct answer.
B
Answer: (B) f(a)=a/2
Question: What is the are of an equilateral triangle of side 16 cm?
(A) 64√5
(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: What percent of 60 is 110?
(A) 133 1⁄3
(B) 75
(C) 183.33
(D) 33 1⁄3
(E) 25
Rationale: % of 60 is 110?
= 110/60 = 11/6 = 183.33%
Thus C is the correct answer.
Answer: (C) 183.33
Question: When a parabola represented by the equation y - 2x 2 = 8 x + 5 is translated 3 units to the left and 2 units up, the new parabola has its vertex at
(A) (-5 , -1)
(B) (-5 , -5)
(C) (-1 , -3)
(D) (-2 , -3)
(E) None
Rationale: Solution
First rewrite y - 2x 2 = 8 x + 5 as
y = 2x 2 + 8 x + 5
Complete square and determine vertex.
y = 2(x 2 + 4x + 4) - 8 + 5
= 2(x + 2) 2 - 3
vertex at (- 2 , - 3)
If parabola is translated 3 units to the left and 2 units up its vertex is also translated 3 units to the right and 2 units up .
vertex after translations is at: (-2 - 3 , - 3 + 2) = (-5 , -1)
Answer A
Answer: (A) (-5 , -1)
Question: A train running at 35 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
(A) 90m45m
(B) 100m50m
(C) 50m45m
(D) 100/3 m200/3
(E) none of these
Rationale: A train running at 35 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
Distance = Speed*time
It's probably best to convert to meters so we can find the length of the platform.
Distance = 35000 meters/h * 18 seconds*(1/60*60)
Distance =(35000*18 / [3600] ) = 175m
I'm not sure how we take the length of the train into account (if we do at all) to solve this problem. For example, If we were measuring by the time the very front of the train passed one end of the platform to the time the very front of the train passed the other end, the result would be different than if we counted when the very front of the train passed one end of the platform to the time the back side of the train passed the end.
As for the problem involving the man, the man is moving forward at a speed of 5km/h while the train is moving forward at a speed of 35km/h. Therefore, the train is moving past the man at a total speed of 30km/h.
distance = speed * time
distance = 30km/h * 12 seconds
distance (length of train) = 100 m
We know the length of the train is roughly 100m and the distance covered passing the platform was 175m. However, The platform isn't 125m long - it is 125m minus the length of the train long (or so I think) which is 175-100 or 75m. Both of these answers are not in any answer.
ANSWER: E) none of these
Answer: (E) none of these
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 19
(B) 17
(C) 10
(D) 12
(E) 13
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds. Answer: D
Answer: (D) 12
Question: Sarah makes handmade jewelry. This month she has created 253 necklaces. If she distributes her jewelry evenly to the 6 jewelry stores in town, how many necklaces remain with her?
(A) 0 necklaces
(B) 1 necklace
(C) 2 necklaces
(D) 3 necklaces
(E) 4 necklaces
Rationale: We need to find the first number that is divisible by 6 that occurs before 253.
In order to divide the sum in 6 parts, the amount must be divisible by 6.
Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3
We need to make this number even in order for it to be divisible by 2. So we must subtract an even number
Sum of digits of 253 = 10 and 9 is divisible by 3 and subtracting 1 yields an even number
Hence, we remove 1 from this number for it to be divisible by 6
Correct Option: B
Answer: (B) 1 necklace
Question: Tough and Tricky questions: Probability.
Medical analysts predict that one over five of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?
(A) 16/81
(B) 8/27
(C) 2/3
(D) 61/125
(E) 65/81
Rationale: At the end of each day we will have 4/5 alive. So after 3 days we will have (4/5)^3 people alive. Therefore, fraction of dead people will be 1-(4/5)^3=61/125.
The correct answer is D.
Answer: (D) 61/125
Question: The perimeter of one square is 48 cm and that of another is 24 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√4
(B) 13√2
(C) 13.4√2
(D) 12√4
(E) 13√9
Rationale: 4a = 48 4a = 24
a = 12 a = 6
a2 = 144 a2 = 36
Combined area = a2 = 180 => a = 13.4
d = 13.4√2
Answer: C
Answer: (C) 13.4√2
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?
(A) 767 km
(B) 176 km
(C) 960 km
(D) 199 km
(E) 986 km
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer:C
Answer: (C) 960 km
Question: When 2 dices tossed, what is the probability that 2 numbers faced have difference 2?
(A) 1/9
(B) 2/9
(C) 1/3
(D) 4/9
(E) 5/9
Rationale: Combinations are (1,3), (2,4), (3,5), (4,6), (3,1), (4,2), (5,3), (6,4)
So, total = 8
Hence, Probability = 8/36 = 2/9
answer:B
Answer: (B) 2/9
Question: A Pharmacy company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 8 hrs and a machine of type S does the same job in 4 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 2
(D) 9
(E) 12
Rationale: Rate of machine R =1/8
Rate of machine S =1/4
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/8 +x/4 =1/2
3x/8=1/2
x=8/6=1.3=2
So no of machine R is 2
Answer C
Answer: (C) 2
Question: Eggs are sold in packages of six or eleven only. If Doris bought 79 eggs exactly, what could be the number of large packs Doris bought?
(A) 6.
(B) 2.
(C) 3.
(D) 5.
(E) 4.
Rationale: No strategy involved. Simple question demanding fast calculation.
11x5 = 55 => 79-55=24=> 24/6 is an integer
Ans D. 5.
Good luck
Answer: (D) 5.
Question: What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?
(A) 196
(B) 630
(C) 1260
(D) 2520
(E) 2540
Rationale: L.C.M of 12, 18, 21, 30
= 2 * 3 * 2 * 3 * 7 * 5 = 1260
Required number = 1260/2 = 630.
ANSWER:B
Answer: (B) 630
Question: The perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 38 cm2
(B) 55 cm2
(C) 65 cm2
(D) 45 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 44/2 = 55 cm2
Answer:B
Answer: (B) 55 cm2
Question: How much interest can a person get on Rs. 6280 at 15.5% p.a. simple interest for a period of five years and six months?
(A) 5353.72
(B) 5353.71
(C) 5353.7
(D) 5353.73
(E) 5353.74
Rationale: I = (6280 * 5.5 * 15.5)/100
= (6280 * 11 * 31)/(100 * 2 * 2)
= Rs. 5353.7
Answer: C
Answer: (C) 5353.7
Question: Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 40 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
(A) 4:5
(B) 9:25
(C) 5:4
(D) 25:9
(E) Cannot be determined from the information provided
Rationale: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B
Time A = 2*pi*25/Speed A
Time B = 2*pi*20/Speed B
Since the times are same,
50pi/Speed A = 40pi/Speed B
SpeedA/Speed B = 50pi/30pi = 5/4
Correct Option: C
Answer: (C) 5:4
Question: What is the dividend. divisor 19, the quotient is 7 and the remainder is 6
(A) 136
(B) 137
(C) 138
(D) 139
(E) 140
Rationale: D = d * Q + R
D = 19 * 7 + 6
D = 133 + 6
D = 139
Answer: (D) 139
Question: If log 27 = 1.731, then the value of log 9 is:
(A) 0.934
(B) 0.945
(C) 0.954
(D) 1.156
(E) 0.987
Rationale: log 27 = 1.731
log (33 ) = 1.731
3 log 3 = 1.731
log 3 = 0.578
log 9 = log(32 ) = 2 log 3 = (2 x 0.578) = 1.156.
Answer: Option D
Answer: (D) 1.156
Question: A certain sum of money doubles itself in 17 years in how much many years will it trible itself at the same rate?
(A) 20 years
(B) 76 years
(C) 88 years
(D) 44 years
(E) 34 years
Rationale: 100 ---- 100 --- 17
100 --- 17
--------------------
300 ---- 34 years
Answer: E
Answer: (E) 34 years
Question: Find the average of the series : 312, 162, 132, 142 and 122?
(A) 172
(B) 616
(C) 157
(D) 154
(E) 174
Rationale: Average
= (312 + 162 + 132 + 142 + 122)/5 = 870/5
= 174
Answer:E
Answer: (E) 174
Question: A merchant marks goods up by 75% and then offers a discount on the marked price. The profit that the merchant makes after offering the discount is 57.5%. What % discount did the merchant offer?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Let P be the original price of the goods and let x be the rate after the markup.
(1.75P)*x = 1.575P
x = 1.575/1.75 = 0.9 which is a discount of 10%.
The answer is A.
Answer: (A) 10%
Question: The cost of 15 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
(A) Rs 52.50
(B) Rs 56
(C) Rs 58.50
(D) Rs 64.75
(E) None of these
Rationale: Explanation :
Let the required cost be Rs. x. Then,
More packets, More cost (Direct Proportion)
More weight, More cost (Direct Proportion)
Packets 15 : 27
Weight 900 : 1000 :: 28 : x
(15 x 900 x x) = (27 x 1000 x 28)
x = (27 x 1000 x 28) /15 x 900
= 56
Answer B
Answer: (B) Rs 56
Question: What is the greatest of 3 consecutive integers whose sum is 24 ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 24;
=> 3n = 21;
=> n = 7
The greatest of the three numbers is therefore 7 + 2 = 9 Answer: D
Answer: (D) 9
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 18:15
(C) 18:19
(D) 18:13
(E) 18:12
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer: A
Answer: (A) 18:11
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
(A) 11
(B) 14
(C) 12
(D) 18
(E) 16
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.Answer: C
Answer: (C) 12
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 35% profit?
(A) 16.39
(B) 16.33
(C) 16.35
(D) 17.01
(E) 16.32
Rationale: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 135% of Rs. 630 = 135/100 * 630 = Rs. 850.50.
S.P. per kg = 850.50/50 = Rs. 16.38 = 16.30.
Answer: D
Answer: (D) 17.01
Question: The value of log5(1/ 125) is
(A) 3
(B) -3
(C) 1/3
(D) -1/3
(E) None
Rationale: Solution
Let log5(1/125)	= n.
Then, 5n= 1/125
‹=›5n =5-3
n= -3.
Answer B
Answer: (B) -3