RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
A.50
B.60
C.70
D.80
Answer: D.80
Explanation: kk is 3-digit integer. Any 3 digit integer can be expressed as 100a+10b+c100a+10b+c.
Now, we are told that (100a+10b+c)+99=100c+10b+a(100a+10b+c)+99=100c+10b+a --> 99c−99a=9999c−99a=99 --> c−a=1c−a=1 --> there are 8 pairs of cc and aa possible such that their difference to be 1: (9,8), (8,7), ..., and (2,1) (note that aa can not be 0 as kk is 3-digit integer and its hundreds digit, aa, is more than or equal to 1).
Also, bb, tens digit of kk, could tale 10 values (0, 1, ..., 9) so there are total of 8*10=80 such numbers possible.
Example:
102 - 201;
112 - 211;
122 - 221;
...
899 - 998.
Answer: D.
Question: If two dice are thrown together, the probability of getting a square number on both the dice is
A.5/12
B.1/3
C.1/4
D.1/12
Answer: D.1/12
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting a sqaure number on both the dice.
P(E) = 3/36 = 1/12.
D)
Question: Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 13 years is Rs.8160, how much money did he borrow?
A.s.8500
B.s.6375
C.s.8000
D.s.9000
Answer: B.s.6375
Explanation: using the formula S.I=P*T*R/100
(x*6*3/100)+(x*9*5/100)+(x*13*5/100)=8160
x=6375
i.e money borrowed is Rs.6375
ANSWER:B
Question: 100 identical coins each with probability 'pp' showing up heads & tossed. If 0
A.23/113
B.25/114
C.51/101
D.56/117
Answer: C.51/101
Explanation: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Question: What is the largest 4 digit number exactly divisible by 88?
A.9944
B.9999
C.9988
D.9900
Answer: A.9944
Explanation: Largest 4 digit number = 9999
9999 ÷ 88 = 113, remainder = 55
Hence largest 4 digit number exactly divisible by 88
= 9999 - 55 = 9944
Answer: Option A
Question: In how many ways can the letters of the word AFRAID be rearranged such that the vowels always appear together?
A.6!/2!
B.3!*3!
C.4!/2!
D.(4! *3!)/2!
Answer: D.(4! *3!)/2!
Explanation: In the word ABACUS , there are 3 vowels - 2 A's and I
Number of ways the letters of word AFRAID be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 35∘, the temperature of Friday was :
A.43∘
B.40∘
C.38∘
D.30∘
Answer: A.43∘
Explanation: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 35. So T+W+Th=(152-35)=117
T+W+Th+F=(4×40)=160
F = (160-117)=43∘
Correct Option: A
Question: How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
A.5
B.6
C.13
D.18
Answer: C.13
Explanation: Explanation:
Required numbers are 24, 30, 36, 42, ..., 96
This is an A.P. in which a = 24, d = 6 and l = 96
Let the number of terms in it be n.
Then tn = 96 a + (n - 1)d = 96
24 + (n - 1) x 6 = 96
(n - 1) x 6 = 72
(n - 1) = 12
n = 13
Required number of numbers = 13.
ANSWER C
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
A.50
B.88
C.77
D.66
Answer: A.50
Explanation: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer:A
Question: What is the smallest possible common multiple of three integers, all larger than 21?
A.27.
B.54.
C.846.
D.22
Answer: D.22
Explanation: The Least common positive multiple would be for the immediate least number(s) after 21 i.e 22.
Since nowhere is it stated that the three integers must be different, the integers could be 22,22 and 22... leading to least possible positive common multiple to be 22. Answer D.
Question: .
On dividing a number by 357, we get 41 as remainder. On dividing the same number 17, what will be the remainder ?
A.0
B.7
C.5
D.8
Answer: B.7
Explanation: Let x be the number and y be the quotient. Then,
x = 357 x y + 41
= (17 x 21 x y) + (17 x 2) + 7
= 17 x (21y + 2) + 7)
Required remainder = 7.
Answer: Option B
Question: A and B entered into a partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs.760. What is A's share in the profit?
A.310
B.320
C.330
D.340
Answer: C.330
Explanation: Ratio of the initial capital of A and B = 4 : 5
Hence we can take the initial capitals of A and B as 4x and 5x respectively
Ratio in which profit will be divided
=((4x)3)+(3/4)×(4x)7 :((5x)3)+4/5×(5x)7
=(12+21):(15+28)
=33:43
A's share =760×33/76=330
Answer is C.
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
A.16
B.18
C.24
D.19
Answer: C.24
Explanation: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer: C
Question: If the product of the integers from 1 to n is divisible by 686, what is the least possible value of n?
A.7
B.14
C.21
D.28
Answer: C.21
Explanation: 686 = 7 x 7 x 7 x 2
N must include at least 7, 2*7, and 3*7.
The answer is C.
Question: Due to construction, the speed limit along an 5-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A. 3.12
B. 8
C. 10
D. 15
Answer: A. 3.12
Explanation: Old time in minutes to cross 5 miles stretch = 5*60/55 = 5*12/11 = 5.45
New time in minutes to cross 5 miles stretch = 5*60/35 = 5*12/7 = 8.57
Time difference = 3.12
Ans:A
Question: .002/?= .01
A..2
B..09
C..009
D..0009
Answer: A..2
Explanation: Let .002/x = .01;
Then x = .002/.01
= .2/1
= .2
Answer is A
Question: If two integers between –5 and 3, inclusive, are chosen at random, which of the following is most likely to be true?
A.The sum of the two integers is even
B.The sum of the two integers is odd
C.The product of the two integers is even
D.The product of the two integers is odd.
Answer: C.The product of the two integers is even
Explanation: 1. The sum of the two integers is even and 2 sum of two integers odd
for sum to be odd -- 5c1*4c1/9c2 = 20/36 thus for even 1-(20/36) = 16/36
3,4 product of two integers even/odd --
for integers to be odd ---- 5c2/9c2 = 52/72 for even 1-52/72 = 20/72
5 for product to be negative -- 0 will not be taken into account. Hence 8 numbers is the set.
5c1 * 3c1/ 8c2 = 15/28
thus comparison is between b 20/36, c 52/72 e 15/28
C is greatest since 52 is much closer to 72 hence much greater than 1/2. 20/36 and 15/28 are much closer to 1/2 though.
Thus C.
Question: 6x − 12 = 6y
6y + 6x = 18
Which of the following is the number of solutions to the system of equations shown above?
A.More than three
B.Exactly three
C.Exactly two
D.Exactly one
Answer: C.Exactly two
Explanation: 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
6y + 6x = 18
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 5
=> x=2.5
y=.5
Therefore , the given system will have Exactly one solution
Answer : C
Question: There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?
A. 17 B. 29 C. 23 D. 31
A.17
B.29
C.23
D.31
Answer: B.29
Explanation: (7429/12673) = 17/29 Fourth Number is 29
ANSWER:B
Question: Four pipes fill a cistern in 15,20,30 and 60 hours.The first was opened at 6 am,the second at 8 am,third at 10 am and fourth at noon.When will the reservoir be full?
A.1PM
B.2PM
C.3PM
D.4PM
Answer: B.2PM
Explanation: If the cistern was filled after x hrs from 6 AM, Then
x/15 + (x-2)/20 + (x-4)/30 +(x-6)/60 =1
solving , we get
x=8 hrs
2PM
ANSWER:B
Question: John and David were each given X dollars in advance for each day they were expected to perform at a community festival. John eventually performed on all 40 days of the festival, while David performed on 5 fewer days than John performed. If David 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.10Y
B.12Y
C.15Y
D.18Y
Answer: C.15Y
Explanation: Both of them were given X $ each
David to adjust Y $ in advance to John
So David now has (X-Y)$ and John has (X+Y) $ such that their daily rate becomes same
So Rate of David= Rate of John
Also , David works for 35 days and John works for full 40 days
(X-Y) / 35 = (X+Y) / 40
Solving 40x-40y=35x+35y =>5x=75y => x=75/5y
X= 15Y
Answer : C
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
A.22
B.88
C.12
D.87
Answer: C.12
Explanation: D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer: C
Question: The salaries of A,B and C are in the ratio 2:3:5. If the increments of 15%,10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
A.11:23:55
B.23:33:60
C.15:45:66
D.23:59:77
Answer: B.23:33:60
Explanation: Let A = 2k
B =3k
C = 5k
A's new salary = 115/00 of 2k = 23/10 k
B's new salary = 110/100 of 3k = 110/100 * 3k = 33/10 k
C's new salary = 120/100 of 5k = 120/100 * 5k = 6k
New ratio = 23k/10 : 33k/10 : 6k = 23:33:60
Answer is B
Question: A 6% stock yields 8%.The market value of the stock is :
A.Rs. 48
B.Rs. 75
C.Rs. 96
D.Rs. 133.33
Answer: B.Rs. 75
Explanation: Solution
For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs.(100/8x6) = Rs. 75.
∴ Market value of Rs.100 stock = Rs. 75.
Answer B
Question: If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM ?
A.32
B.76
C.29
D.27
Answer: A.32
Explanation: Explanation:
The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.
The first 24 of these words will start with A.
Then the 25th word will start will CA _ _ _.
The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.
The next word starts with CH and then A, i.e., CHA _ _.
The first of the words will be CHAMS. The next word will be CHASM.
Therefore, the rank of CHASM will be 24+6+2= 32
Answer: A) 32
Question: If 10^(c-1)< 0.000125 <10^c, what is the value of an integer c?
A.-4
B.-3
C.-2
D.3
Answer: B.-3
Explanation: -> Multiply 10^6- > (10^6){10^(c-1)}<125<(10^6)(10^c) -> 125 is bigger than 100
-> (10^6)(10^(c-1))=100 -> 10^(6+c-1)=10^2, c+5=2 -> c=-3
Thus, the answer is B
Question: The average of the two-digit numbers, which remain the same when the dibits inter-change their positions, is
A.88
B.28
C.55
D.25
Answer: C.55
Explanation: Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99) / 9
=( (11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55) / 9
= (4 * 110 + 55)/9 = 495 / 9 = 55
Answer: C
Question: If there is exactly one root of the equation 2x^2 + ax + b, where a and b are positive constants, what is b in terms of a?
A.a/2
B.a
C.3a/2
D.a^2/8
Answer: D.a^2/8
Explanation: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here b = a
c= b
a = 2
substituting these values in 1, we have
a^2 = 8b => b =a^2/8
Answer is D.
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 40% Vermouth by volume. How many ounces of Gin must he add?
A.0
B.n/3
C.3n/5
D.5n/6
Answer: A.0
Explanation: 4 ounces is vermouth
6 ounces of gin...
Total volume 10.
To make vermouth account for 40% of total volume the new volume must be....
x*0.4=4
x=10 ounces....
So now you see that he must add 0 ounces of gin...
Plug in 0 for n in the answer choices and look for answer 0
A
Question: If n = 30! + 25, then n is divisible by which of the following?
I. 25
II. 27
III. 29
A.None
B.I only
C.II only
D.I and II
Answer: B.I only
Explanation: 25 divides 30! so 25 also divides 30! + 25.
27 and 29 divide 30! so they do not divide 30! + 25.
The answer is B.
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.288
B.375
C.267
D.298
Answer: B.375
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: B
Question: Insert the missing number
2, 4, 8, 16, ..., 64, 128, 256
A.36
B.35
C.32
D.33
Answer: C.32
Explanation: series is 2* Previous Number.
ANSWER:C
Question: Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer E between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
A.12
B.15
C.17
D.E=18
Answer: D.E=18
Explanation: Since we are concerned with integers between 1 and 20, write down the primes till 40.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
(you should be very comfortable with the first few primes... )
2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)
2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)
2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)
2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)
2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.
Answer (D).
Question: The price of 2 skirts and 4 shirts is Rs. 1600. With the same money one can buy 1 skirt and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
A.Rs. 2300
B.Rs. 2400
C.Rs. 2420
D.Rs. 2460
Answer: B.Rs. 2400
Explanation: Let the price of a skirt and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
B
Question: A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.
A.80 cm
B.10 cm
C.70 cm
D.60 cm
Answer: B.10 cm
Explanation: The volume of a rectangular prism is given by
area of base ? height
The rate at which the tank is being filled is 1 liter per minute which we need to convert
1 liter = 1 dm3
But 1 dm = 10 cm. Hence
1 liter = (10 cm)3 = 1000 cm3
The height h of the water is related to the volume by
volume = area of base ? h
In one minute the volume increases by 1 liter or 1000 cm3 and the height increases by
h = volume / area of base = 1000 cm3 / 100 cm2 = 10 cm
correct answer B
Question: A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?
A.576
B.800
C.726
D.484
Answer: C.726
Explanation: (4/15) * A = (2/5) * B
A / B = 3 / 2
Therefore A's share is = (1210 * (3/5)) = 726
Ans - C
Question: How many randomly assembled people do u need to have a better than 50% probability that at least 1 of them was born in a leap year?
A.3
B.9
C.27
D.54
Answer: A.3
Explanation: Prob[at least one of them was born in a leap year] > 50%
Since P(A) = 1 - P(A')
1 - Prob[none of them was born in a leap year] > 1/2
Prob[none] - 1 < -1/2
Prob[none] < 1/2
Assume that there are n people.
Prob[none] = (3/4)^n
(3/4)^n < 1/2
3^n < (4^n)/2
3^n < (2^2n)/2
3^n < 2^(2n-1)
If n = 3, 3^3 < 2^5 is true
A is the answer
Question: A company has found that when x units of a product are manufactured and sold, its revenue is given by x 2 + 100 x dollars and its costs are given by 240 x + 500 dollars. How many units must be produced and sold to make a profit of 10,000 dollars? (HINT: profit = revenue - costs)
A.192
B.193
C.194.
D.195
Answer: C.194.
Explanation: Let us use profit = revenue - costs to find a formula for the profit P
P = ( x 2 + 100 x ) - ( 240 x + 500 )
Substitute P in the above equation by 10,000 dollars to obtain
10000 = x 2 - 140 x - 500
Write the equation in standard form and solve for x
x 2 - 140 x - 10500 = 0
Solve the above equation for x
x = 194.10 and x = -54.01
The number of units to produce must be positive, so
x = 194.
As an exercise, check that for the above value of x the profit is approximately (because of the rounding) equal to 10,000.
Answer C
Question: If |5x-20| = 100, then find the sum of the values of x?
A.1
B.-2
C.8
D.-3
Answer: C.8
Explanation: |5x-20| = 100
5x-20 = 100 or 5x-20 = -100
5x = 120 or 5x = -80
x = 24 or x = -16
sum = 24-16 = 8
Answer is C
Question: The average weight of 25 boys sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the boys decreased by 5 kg. Find the average weight of first 25 boys?
A.150
B.154
C.176
D.182
Answer: C.176
Explanation: 25x + 46 = 26(x – 5)
x = 176
C
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is?
A.4/9
B.5/9
C.2/9
D.3/8
Answer: B.5/9
Explanation: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer:B
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
A.29
B.86
C.25
D.18
Answer: B.86
Explanation: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86
Answer:B
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 36,000, what will be the amount A receives?
A.15120
B.14500
C.14900
D.14300
Answer: A.15120
Explanation: Total amount invested = 50000
Assume that investment of C =x.
Then investment of B =5000+x,
Investment of A =4000+5000+x=9000+x
x+5000+x+9000+x=50000
⇒3x+14000=50000
⇒3x=50000–14000=36000
⇒x=36000/3=12000
Investment of C =x=12000
Investment of B =5000+x=17000
Investment of A =9000+x=21000
Ratio of the investment of A, B and C
=21000:17000:12000
=21:17:12
Share of A = Total profit ×21/50
=36000×21/50=15,120
Answer is A.
Question: There are 60 slots around a circle,numbered 1 to 60. A man starts fromthe first slot and jumps to the 5th slot.From there he jumps to the 9th slot andso on. In which slot will he land in his 2200th jump?
A.1
B.5
C.41
D.45
Answer: C.41
Explanation: every 15th jump, he comes back to 1st position
so, 2200/15 = Remainder 10
Hence 10th position is 41st slot
ANSWER:C
Question: The age of the daughter is same as the digit in the mother's age, but in reverse order. In thirteen years mother will be twice as old as daughter will be then. what is the difference in their current age ?
A.15
B.23
C.27
D.46
Answer: C.27
Explanation: daughter's age= 10x+y
so mother's age= 10y+x..
after 13 years , 10x+y+13=2*(10y+x+13)....
so 13+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=4... so ages are 41 and 14 and ans as found correctly by u is C..27
Question: What is the solution of the equations x - y = 5 and 5(x + y)-1 = 2 ?
A.x = 3.75, y = 1.25
B.x = 1, y = 0.1
C.x = 2, y = 1.1
D.x = 1.2, y = 0.3
Answer: A.x = 3.75, y = 1.25
Explanation: Answer
x - y = 5 ...(i)
and 11(x + y)-1=2
⇒ 5/ (x + y) = 2
⇒ 2(x + y) =5
⇒ x + y = 5/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 3.75
and y = 1.25
Correct Option: A
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in?
A.144 min
B.250 min
C.196 min
D.100 min
Answer: A.144 min
Explanation: Let the slower pipe alone fill the tank in x minutes
Then, faster pipe will fill it in x/3 minutes
1/x + 3/x = 1/36
4/x = 1/36
x = 144 min
Answer is A
Question: Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $33. What was the percentage profit?
A.5%
B.6%
C.8%
D.10%
Answer: D.10%
Explanation: A dozen toys cost $360, so each toy cost $30.
selling price / cost price = 33/30 = 1.1
The percentage profit is 10%.
The answer is D.
Question: If 3^z is a factor of 52!, which of the following could be the value of z?
I. 22
II. 21
III. 23
A.I ONLY
B.II ONLY
C.III ONLY
D.BOTH I AND II
Answer: C.III ONLY
Explanation: 3^z is a factor of 52!, what values can z take.
Powers of 3 in 52! = [52/3] + [52/9] +[52/27] , where [x] is the integral part of x
Powers of 3 in 52! = 17 + 5 + 1 = 23
Hence the maximum value of 3^z in 52! = 3^23
Only Statement III satisfies
Correct Option: C
Question: How many pairs of letters are there in the word 'CASTRAPHONE' which have as many letters between
them in the word as in the alphabet?
A.8
B.7
C.6
D.4
Answer: D.4
Explanation: Looking into the alphabets there are four such pairs namely ON,EH,ST,TO.
Answer: D
Question: A train speeds past a pole in 12 seconds and a platform 160 m long in 17 seconds. Its length is?
A.384
B.360
C.324
D.390
Answer: A.384
Explanation: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 12 => y = x/12
x + 160 / 17 = x / 12
x = 384 m.
Answer:A
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked three 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
A.280
B.300
C.240
D.350
Answer: C.240
Explanation: Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.
Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).
Jill has worked for 3 days -> 80*3=240.
This matches answer choice C.
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability E that each number is different ?
A.A.18/25
B.B.4/5
C.C.81/100
D.D.9/10
Answer: A.A.18/25
Explanation: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability E= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Question: Income and expenditure of a person are in the ratio 5:4. If the income of the person is Rs.18000, then find his savings?
A.Rs.3600
B.Rs.3689
C.Rs.3615
D.Rs.3628
Answer: A.Rs.3600
Explanation: Let the income and the expenditure of the person be Rs.5x and Rs.4x respectively.
Income, 5x = 18000 => x = 3600
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs.3600.
Answer: A