mathewhe/aqua_rat huggingface dataset:
Question: Amanda sees a sale for 30% off all items, she sees a dress on sale that originally cost $50. How much will it cost Amanda to buy the dress after the sale amount of 30% has been take off?
(A) $40
(B) $35
(C) $50
(D) $65
(E) $15
Rationale: Final number = original number - 30%(original number) = 50 - 30%(50) = 50 - 15 = $35.
Answer B
Answer: (B) $35
Question: A car rental company charges for mileage as follows: x dollars per mile for the first n miles and x + 1 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
(A) d( x + 1) – n
(B) xn + d
(C) xn + d( x + 1)
(D) x( n + d) – d
(E) (x + 1)( d – n)
Rationale: Cost of mileage for the first n miles = nx
Cost of mileage for the next d-n miles = (d-n)(x+1)
Total cost
= nx + (d-n)(x+1)
= nx + dx+d-nx-n
= dx+d-n
= d(x+1) - n
Answer A
Answer: (A) d( x + 1) – n
Question: What is the smallest possible common multiple of three integers, all larger than 53?
(A) 27.
(B) 54.
(C) 846.
(D) 19,656.
(E) 21,924.
Rationale: The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54.
Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer B.
Answer: (B) 54.
Question: John makes $60 a week from his job. He earns a raise and now makes $80 a week. What is the % increase?
(A) 16%
(B) 33.33%
(C) 17%
(D) 17.61%
(E) 17.56%
Rationale: Increase = (20/60)*100 = (2/6)*100 = 33.33%.
B
Answer: (B) 33.33%
Question: 125.62+6.325+14.4=?
(A) 222.569
(B) 287.36
(C) 146.345
(D) 125.69
(E) 784.36
Rationale: 125.62
6.325
14.4
----------
146.345
Answer is C
Answer: (C) 146.345
Question: Solve for x: 2x â€“ y = (3/4)x + 5.
(A) (y + 6)/5
(B) 4(y + 5)/5
(C) (y + 6)
(D) 4(y - 6)/5
(E) 5/4(y-6)
Rationale: Solution:
2x â€“ y = (3/4)x + 5.
or, 2x - (3/4)x = y + 5.
or, (8x -3x)/4 = y + 5.
or, 5x/4 = y + 5.
or, 5x = 4(y + 5).
or, 5x = 4y + 20.
or, x = (4y + 20)/5.
Therefore, x = 4(y + 5)/5.
correct answer B
Answer: (B) 4(y + 5)/5
Question: The ratio of the incomes of A and B is 2:3 and the ratio of their expenditure is 1:2. If at the end of the year, each saves $500 then the income of A is?
(A) $1000
(B) $1500
(C) $1200
(D) $900
(E) $1100
Rationale: Let the income of A and B be $2x and $3x
Let their expenditures be $y and $2y
2x-y = 500-------1)
3x-2y = 500-------2)
From 1) and 2)
x = 500
A's income = 2x = 2*500 = $1000
Answer is A
Answer: (A) $1000
Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
B
Answer: (B) 1
Question: John and Cindy were each given X dollars in advance for each day they were expected to perform at a community festival. John eventually performed on all 20 days of the festival, while Cindy performed on 5 fewer days than John performed. If Cindy gives John y dollars of her advance payment so that they would have each received the same daily rate, what was John paid in advance, in terms of Y?
(A) 8Y
(B) 7Y
(C) 10Y
(D) 12Y
(E) 5Y
Rationale: Both of them were given X $ each
Cindy to adjust Y $ in advance to John
So Cindy now has (X-Y)$ and John has (X+Y) $ such that their daily rate becomes same
So Rate of CIndy= Rate of John
Also , Cindy works for 15 days and John works for full 20 days
(X-Y) / 15 = (X+Y) / 20
Solving 20x-20y=15x+15y =>5x=35y => x=35/5y
X= 7Y
Answer : B
Answer: (B) 7Y
Question: A student completes a 3 part exam as follows. The student completes sections A in 18 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour?
(A) 4:3
(B) 5:4
(C) 6:5
(D) 7:6
(E) 8:7
Rationale: The time spent on section B and section C is 21 minutes each.
The ratio of C to A is 21:18 = 7:6
The answer is D.
Answer: (D) 7:6
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 145, what is the difference between the ages of Patrick and Monica?
(A) 27
(B) 48
(C) 45
(D) 72
(E) 18
Rationale: Ages of P and Mi=3x+5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=47x=145
x=3
Difference if ages of Pa and Mo=25x-9x=16x=16*3=48
Answer B
Answer: (B) 48
Question: Adam's mother is 26 years older than him. Next year, however, she will be 3 times older than her son. How old is Adam's mother?
(A) 35 years
(B) 36 years
(C) 37 years
(D) 38 years
(E) 39 years
Rationale: At the present
Adam is x years old.
Adam's mother is y=x+26 years old.
Next year
Adam will be x+1 years old.
Adams mother will be y+1=3 (x+1) years old.
If we combine the two equations,
y=x+26, and
y+1=3 (x+1), then
x+26+1=3x+3
2x=27-3
2x=24
x=12
This is Adam's age at the moment. Since his mother is 26 years older than him, her age is 12+26=38.
ANSWER: D
Answer: (D) 38 years
Question: If 'y' is a positive integer exactly divisible by 4 or 5 but not divisible by 8.What could possibly be the value of 'y' ?
(A) 40
(B) 80
(C) 20
(D) 24
(E) 36
Rationale: 40 and 80 are both divisible by 4 and 5 but also by 8. so they are not the right answer.
24 and 36 are both clearly not divisible by 5(not correct)
20 is both divisible by 4 and 5 but not by 8.
answer : (C)
Answer: (C) 20
Question: Lola has $240.00 in her checking account. She spent $180.00. What percentage does she have left in her account ?
(A) 75 %
(B) 50 %
(C) 40 %
(D) 55 %
(E) None of these
Rationale: Explanation :
Amount left : 240 - 180 = 60
Amount left percentage = (60/240 x 100) %
= 25 %
Answer : E
Answer: (E) None of these
Question: Solution Y is 20 percent liquid X and 80 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
(A) 20%
(B) 21 1/2%
(C) 22%
(D) 24%
(E) 25%
Rationale: In 8 kilograms of solution Y there are 0.2*8=1.6kilograms of solution X;
After 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.2*2=0.4 kilograms of solution X are added, so in the new solution of 8 kilograms there are 1.6+0.4=2 kilograms of solution X, which is 2/8*100=25% of this new solution.
Answer: E.
Answer: (E) 25%
Question: After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B?
(A) N/15
(B) 7N/8
(C) 14N/15
(D) N/5
(E) 4N/5
Rationale: 1/4 of tested had infection A, thus N/4 had infection A;
Of those with infection A, 1/2 also had infection B, thus 1/2*N/4 = N/8 had both infections A and B.
Therefore, N - N/8 = 7N/8 did not have both infection A and B.
Answer: B.
Answer: (B) 7N/8
Question: Of the numbers, average of the first five is 16 and that of the last five is 20. if the last number is 20. find the first number?
(A) 20
(B) 0
(C) 24
(D) 26
(E) 28
Rationale: Explanation :
Solution: Let the 6 numbers be a, b, c, d, e and 20. then, given
=> a + b + c + d + e/5 =16
=> b + c + d + e + 20/5 =20
Solve those two equations then we will get a = 0.
.'. first number = 0.
Answer : B
Answer: (B) 0
Question: Mixture A is 10 percent alcohol, and mixture B is 40 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 20 percent alcohol, approximately how many gallons of mixture A are in the mixture?
(A) 1.6
(B) 1.7
(C) 1.8
(D) 1.9
(E) 2.0
Rationale: (40-20)/(20-15) = Qa/Qb
20/10 = Qa/Qb
2/1 = Qa/Qb
Qa = (2/5) * 4 = 8/5 = 1.6 approx
Answer : A
Answer: (A) 1.6
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 200
(B) 205
(C) 204
(D) 209
(E) 300
Rationale: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
=>209
ANSWER D
Answer: (D) 209
Question: A wholesale tea dealer 408 kilograms, 468 kilograms and 516 kilograms of three different qualities of tea. He wants it all to be packed into boxes of equal size without mixing. Find the capacity of the largest possible box?
(A) 50
(B) 36
(C) 24
(D) 12
(E) 20
Rationale: HCF of 408, 468, 516 = 12
ANSWER:D
Answer: (D) 12
Question: If $10,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years?
(A)  compounding annually
(B)  compounding quarterly
(C)  compounding daily
(D)  compounding monthly
(E)  All four of these would produce the same total
Rationale: Answer = C Compounding daily
This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest.
This process will be repeated every day till the amount matures
Compounding annually will give least returns
Answer: (C)  compounding daily
Question: What is the probability that the sum of two dice will yield a 9, and then when both are thrown again, their sum will again yield a 9? assume that each die has 8 sides with faces numbered 1 to 8.
(A) 1/64
(B) 1/36
(C) 1/12
(D) 1/6
(E) 1/3
Rationale: Solution -
Rolling dices is an independent event.
The combinations to get 9 are (1,8), (8,1), (2,7), (7,2), (3,6), (6,3), (4,5), (5,4), and total combinations of both dices is 64.
The probability of getting 9 in first attempt is 8/64=1/8.
Probability of getting 9 again in second attempt = (1/8)*(1/8) = 1/64. ANS A
Answer: (A) 1/64
Question: The greatest number of four digits which is divisible by 7, 10, 40 and 60 is:
(A) 9200
(B) 9300
(C) 9400
(D) 8400
(E) 7400
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 7, 10, 40 and 60 is 4200.
On dividing 9999 by 4200, the remainder is 1599.
Required number (9999 - 1599) = 8400.
ANSWER :D
Answer: (D) 8400
Question: A restaurant spends one quarter of its monthly budget for rent and half of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages?
(A) 23.5%
(B) 32.5%
(C) 35%
(D) 37.5%
(E) 75%
Rationale: let the total budget be 100
as per the question ,
restaurant spends one quarter of its monthly budget for rent = 25
half of the rest for food and beverages = 75/2 =37.5
therefore, percentage spent on food and beverage = 37.5
ANSWER:D
Answer: (D) 37.5%
Question: Out of 420 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
(A) 120
(B) 150
(C) 130
(D) 180
(E) 220
Rationale: n(A)=325,n(B)=175,n(AuB)=420-50=370.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-370=130.
Answer is C
Answer: (C) 130
Question: The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was
(A) 162
(B) 108
(C) 96
(D) 54
(E) None
Rationale: Solution: Let the number of students in the classes be 2x, 3x and 4x respectively;
Total students = 2x+3x+4x = 9x.
According to the question,
(2x+12)/(3x+12) = 8/11
24x+96 = 22x+132
Or, 2x = 132-96
Or, x = 36/2 = 18
Hence, Original number of students,
9x = 9*18 = 162.
Answer: Option A
Answer: (A) 162
Question: Find a 5-digit integer whose value is equal to the sum of the factorials of its own digits.
(A) 40585
(B) 41585
(C) 42585
(D) 44585
(E) 30585
Rationale: factorial values from 0 to 9
0!=1
1!=1
2!=2
3!=6
4!=24
5!=120
6!=720
7!=5040
8!=40320
9!=362880 now given that it is a 5 digit number
so we can eliminate 9! from the count.
but
0-9 numbers can be arranged in 5 digit numbers in 9x9x9x9x9=59049(if repetition)
If not:
9x8x7x6x5=15120
by crosscheck we can eliminate numbers with 1,2,3,6,7,8,9 numbers in twice or thrice or more
40585
4!+0!+5!+8!+5!= 24 + 1 + 120 + 40320 + 120
= 40585
ANSWER:A
Answer: (A) 40585
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) 9
(B) 8
(C) 7
(D) 6
(E) 4
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: A
Answer: (A) 9
Question: By weight, liquid X makes up 0.7 percent of solution P and 1.2 percent of solution Q. If 200 grams of solution P are mixed with 800 grams of solution Q, then liquid X accounts for what percent of the weight of the resulting solution?
(A) 1.2%
(B) 1.1%
(C) 1.0%
(D) 0.9%
(E) 0.8%
Rationale: The number of grams of liquid X is 0.7(200)/100 + 1.2(800)/100 = 1.4 + 9.6 = 11 grams.
11 / 1000 = 1.1%
The answer is B.
Answer: (B) 1.1%
Question: A line has a slope of 3/4 and intersects the point (-12, -39). At which point E does this line intersect the x-axis?
(A) (40,0)
(B) (30,0)
(C) (0,40)
(D) (40,30)
(E) (0,30)
Rationale: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.
You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.
Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.
After substituting the above values, you get c = -30.
Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.
Put y=0 in the above equation of the line and you will get, x=40.
Thus, the point E of intersection is (40,0).
A is the correct answer.
Answer: (A) (40,0)
Question: A bag contains 6 black and 7 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4
(B) 4/3
(C) 4/5
(D) 4/9
(E) 7/13
Rationale: Let number of balls = (6 + 7) = 13.
Number of white balls = 7.
P (drawing a white ball) = 7/13
Hence Answer is E
Answer: (E) 7/13
Question: There can be myriad ways to create a palindrome. One day, I thought of making my own palindrome. I thought of a number and then decided to add the reversed number to it. Sadly, I did not get a palindrome.
So I kept repeating this step and eventually I succeeded in creating a palindrome. I don't know if you can always create a palindrome using this method but I was able to generate one of four digits.
Can you tell me the number at which I started?
(A) 192
(B) 130
(C) 185
(D) 167
(E) 120
Rationale: A
192
I started with the number 192.
Adding the reversed 291 to 192 gave me 483.
Similarly,
483 + 384 = 867
867 + 768 = 1635
1635 + 5361 = 6996
Answer: (A) 192
Question: A man buys an article for rs.27.50 and sells it for rs.28.50. Find the gain value.
(A) 4.12
(B) 3.63
(C) 1.1
(D) 2.58
(E) 5.63
Rationale: . cp=rs27.50, sp=rs 28.50
gain=rs(28.50 –27.50)=rs1.10
Ans: C
Answer: (C) 1.1
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 375
(B) 500
(C) 450
(D) 350
(E) 600
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
ANSWER A
Answer: (A) 375
Question: Eight people went to a restaurant for dinner. Seven of them spent $8 each on their meals and the eighth spent $7 more than the average expenditure of all eight people. What was the total amount of money that the eight people spent?
(A) $72
(B) $75
(C) $78
(D) $81
(E) $84
Rationale: Let T be the total amount of money spent.
7*8 + (T/8 + 7) = T
63 = 7T/8
T = (8*63)/7 = 72
The answer is A.
Answer: (A) $72
Question: The radius of the base of cone is 3 cm and height is 4 cm. Find the volume of the cone?
(A) 12
(B) 75
(C) 97
(D) 15
(E) 91
Rationale: 1/3 * π * 3 * 3 * 4
= 12 π
Answer:A
Answer: (A) 12
Question: In a school 20% of the boys are same in number as 1/4th of the girls. what is the ratio of boys to the girls in the school?
(A) 5:4
(B) 2:3
(C) 1:4
(D) 3:7
(E) 2:5
Rationale: 20% of B = 1/4 G
20B/100 = G/4
B = 5G/4
B/G = 5/4
B:G = 5:4
Answer is A
Answer: (A) 5:4
Question: Find the cube root of 185193.
(A) 33
(B) 57
(C) 99
(D) 17
(E) 01
Rationale: Observe unit digit here is 3 so unit digit of the answer is 7. Now omit 193. Now find after which perfect cube 193 lies. It is 125. So our tenth place is 5. So answer is 57.
Answer:B
Answer: (B) 57
Question: A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3 , then the weight of the pipe is
(A) 3.6 kg
(B) 3.696 kg
(C) 36 kg
(D) 36.9 kg
(E) None of these
Rationale: Explanation:
External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron = [(22/7) × (42 - 32) × 21]cm3 = 462 cm3
Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg
Answer: B
Answer: (B) 3.696 kg
Question: The Smallest number which when diminished by 7, is divisible by 12,16,18,21 and 28 is :
(A) 1008
(B) 1015
(C) 1022
(D) 1032
(E) None of these
Rationale: Solution
Required number = (L.C.M. of 12,16,18,21,28)+7 = 1008 + 7 = 1015. Answer B
Answer: (B) 1015
Question: How many of the positive factors of 24 are not factors of 27
(A) 2
(B) 6
(C) 4
(D) 1
(E) 5
Rationale: factors of 24 - 1, 2, 3, 4, 6, 8, 12,24
factors of 27 -1, 3, 9,27
Comparing both, we have 6 factors of 24 which are not factors of 27- 2,4,6,8,12,24
Answer: B
Answer: (B) 6
Question: There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 60%
(A) 18.75
(B) 19.75
(C) 20.75
(D) 21.75
(E) 24
Rationale: 60*84/100=50.40 lit milk that is 9.60 lit water
let x lit water will be added then
(60+x)*60/100=50.40
so x=18.75
ANSWER:E
Answer: (E) 24
Question: A Mango costs Rs 25 each and a apple costs Rs. 21 each. If I spend Rs 71 on total what is the number of mango I purchased?
(A) 4
(B) 6
(C) 2
(D) 10
(E) 8
Rationale: 2 * 25+ 21 = 71
Answer : 2
Option : C
Answer: (C) 2
Question: 1/2 is what percent of 1/3
(A) 150%
(B) 200%
(C) 250%
(D) 300%
(E) None of these
Rationale: Explanation:
1/2/1/3 * 100 = 1/2 * 3/1 * 100 = 150 %
Option A
Answer: (A) 150%
Question: If 18 men take 15 days to to complete a job, in how many days can 24 men finish that work?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Ans. 10 days
Answer: (A) 10
Question: A box contains four gold coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
(A) 4/5
(B) 3/5
(C) 2/5
(D) 1/5
(E) 3/4
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
A
A
Answer: (A) 4/5
Question: a making a cube with dimension 5*5*5 using 1*1*1 cubes.what is the number of cubes needed to make hollow cube looking of the same shape.
(A) 98
(B) 99
(C) 100
(D) 101
(E) 102
Rationale: 125 1*1*1 small cubes=5*5*5 cubes
because hallow in inner we don't have 3*3*3 cubes
so 125-27=98 cubes required
ANSWER:A
Answer: (A) 98
Question: A can finish a piece of work in 5 days. B can do it in 25 days. They work together for four days and then A goes away. In how many days will B finish the work?
(A) 3 days
(B) 1 day
(C) 2 days
(D) 4 days
(E) 5 days
Rationale: 4/5 + (4 + x)/25 = 1 => x = 1 day
Answer: B
Answer: (B) 1 day
Question: In a 20 litre mixture ratio of milk and water is 3:1.how much milk should added so that mixture ratio Become 4:1?
(A) 3
(B) 2
(C) 8
(D) 6
(E) 5
Rationale: Amount of milk=20×3/4=15 litre and water= 5 litre
Let x litre milk to be added
Then 15+x/5=4/1=15+x=20,x=5
Answer E
Answer: (E) 5
Question: In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,4) and (t,-7). What is the least possible value of the slope of line L?
(A) 6
(B) 2
(C) -2
(D) -6
(E) -5.5
Rationale: We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (-7-4)/(4-2) = -5.5
IMO option E is correct answer.
Answer: (E) -5.5
Question: Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7 meter 65 cm
(A) 45cm
(B) 255cm
(C) 244cm
(D) 55cm
(E) 280cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1575 cm, 1125cm, 765cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 255.
Option B
Answer: (B) 255cm
Question: 12500 shares, of par value Rs. 20 each, are purchased from Ram by Mohan at a price of Rs. 25 each. If Mohan further sells the shares at a premium of Rs. 11 each, find his gain in the transaction.
(A) 75000
(B) 76000
(C) 77000
(D) 74000
(E) 70000
Rationale: Face value of each share = Rs.20
Market value of each share = Rs.25
Number of shares = 12500
Amount required to purchase the shares = 12500 × 25 = 312500
Mohan further sells the shares at a premium of Rs. 11 each
ie, Mohan further sells the shares at Rs.(20+11) = Rs.31 per share
total amount he gets by selling all the shares = 12500 × 31 = 387500
His gain = 387500 - 312500 = Rs.75000
Answer is A.
Answer: (A) 75000
Question: In a box of 7 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
(A) 1/2
(B) 1/5
(C) 2/3
(D) 2/7
(E) 1/7
Rationale: First, there are 5C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 7C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 5C3/7C3=10/35 = 2/7
Answer is D
Answer: (D) 2/7
Question: Two trains of length 100 m and 300 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 70/7 sec
(B) 80/7 sec
(C) 40/7 sec
(D) 100/7 sec
(E) 90/7 sec
Rationale: D
Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 300)/35
= 500/35 = 100/7 sec.
Answer: (D) 100/7 sec
Question: Machine Q and machine B are each used to manufacture 660 sprockets. It takes machine Q 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine Q. How many sprockets per hour does machine Q produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: [Reveal]Spoiler:
TimeB: 660/x
TimeQ: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeQ
660/100+10 => 660/110 = 6=A
Answer: (A) 6
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 27 2/23 %
(B) 33 1/3 %
(C) 30%
(D) 19%
(E) 29%
Rationale: 100
150
------
150-------50
100-------? => 331/3%
ANSWER:B
Answer: (B) 33 1/3 %
Question: For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d d feet from the source is given by the formula S=60k/d^2 60, where k is a constant. If the intensity of the light is 15 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?
(A) 3/20 candles
(B) 1/2 candles
(C) 1 1/3 candles
(D) 2 candles
(E) 3 candles
Rationale: ANS = 3/10
S= 60k/d^2
At 2 feet
15 = 60k/4 so k = 1
At 20 feet
S = 60 *1/20^2 = 3/20
A
Answer: (A) 3/20 candles