RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1290. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
A. 2480
B. 3490
C. 6785
D. 8265
Answer: D. 8265
Explanation: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1290, we get the answer of 8265. (ANS D)
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
11 * 13 * 15 =?
A.89
B.49
C.206
D.38
Answer: C.206
Explanation: C
206
(15 * 13) + 11 = 206
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more thanC. Out of a total profit of Rs. 35,000, B receives :
A.11900
B.14703
C.37798
D.13777
Answer: A.11900
Explanation: Explanation:
Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
B's share = Rs. (35000 * 17/50 ) = Rs. 11,900.
Answer: A)
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 60% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
A. 64%
B. 60%
C. 66%
D. 80%
Answer: A. 64%
Explanation: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.6*0.6 = 0.36. So, the probability that he will be able to attend is 1 - 0.36 = 0.64.
Answer: A.
Question: A chair is bought for Rs.600/- and sold at a loss of 20% find its selling price
A.s.480/-
B.s.550/-
C.s.560/-
D.s.590/-
Answer: A.s.480/-
Explanation: 100 % ------> 600 (100 * 6 = 600)
80 % ------> 540 (80 * 6 = 480)
Selling price = Rs.480/-
A)
Question: A train passes a station platform in 40 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
A.615 m
B.240 m
C.180 m
D.197 m
Answer: C.180 m
Explanation: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/40 = 15 => x
= 180 m
Answer: C
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
A.120 kg in the morning and 240 kg in the afternoon
B.100 kg in the morning and 200 kg in the afternoon
C.110 kg in the morning and 220 kg in the afternoon
D.130 kg in the morning and 260 kg in the afternoon
Answer: A.120 kg in the morning and 240 kg in the afternoon
Explanation: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2xx kilograms. So, the total is x+2x=3x. This must be equal to 360.
3x=360
x=360/3
x=120
Therefore, the salesman sold 120 kg in the morning and 2x120=240 kg in the afternoon.
Answer is A
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
A.277
B.266
C.321
D.500
Answer: D.500
Explanation: P - 340 = (P*4*8)/100
P = 500
Answer: D
Question: In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?
A.5P3/(2!)
B.4P3
C.4^3
D.4P3+3C1*(3!/2!)
Answer: D.4P3+3C1*(3!/2!)
Explanation: Had it asked for all the different nos instead of 1,1,2,3,4 the ans would be: 5P3/2! = 30
In this solution we have also halved (divided by 2!) the numbers containing 2,3 and 4.
The numbers containing 2,3,4 are 6.
Add 6/2 =3 back to 30 and we get the answer i.e. 30+3=33.
Hence D is the answer
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
A.23/35
B.23/39
C.23/36
D.23/32
Answer: A.23/35
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35Answer: A
Question: Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = -2
(II) y = 3
(III) x + y = 0
A.I
B.III
C.II
D.I&II
Answer: C.II
Explanation: y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
C
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 5 years ago?
A.152460
B.214560
C.138214
D.210000
Answer: C.138214
Explanation: population 2 years ago = 176400/(1 + 5/100)^5
Answer is C
Question: In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -3, and b = 8a then which of the following is c equal to?
A.a/12
B.a/8
C.15a
D.8a
Answer: C.15a
Explanation: The sum of the roots is = -b/a = -8a/a = -8. Let the other root be x. Thus, x-3 = -8
x = -5. Again, the product of the roots is -3*-5 = 15. Thus, c/a = 15. c = 15a.
C.
Question: Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd?
A.15%
B.25%
C.35%
D.50%
Answer: A.15%
Explanation: About half the multiples of seven will be odd while all the multiples of eight are even.
The percentage of odd numbers is about (1/2)(300) / 1000 = 15%
The answer is A.
Question: If a college has 15 staff for every 700 students, then what is the number of staff for 1400 students?
A.30
B.14
C.12
D.17
Answer: A.30
Explanation: 15/700=x/1400
x = 30
Answer is A
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.160. Find the unknown rate of two blankets?
A.420
B.550
C.490
D.450
Answer: B.550
Explanation: 10 * 160 = 1600
3 * 100 + 5 * 150 = 1050
1600 – 1050 = 550
Answer:B
Question: X is a prime number bigger than 10. Also, Y = X+X^3+X^5+X^7. What is definitely true about Y?
A.Y is a prime number.
B.Y is odd.
C.Y is even.
D.Y is divisible by 3.
Answer: C.Y is even.
Explanation: Assume X= 11 (Since there can be only one unique answer)
Therefore Y= 11 + 11^3 + 11^5 + 11^7
Y=[ Odd + Odd ] + [Odd +Odd]
Y= Even + Even
Y= Even
Ans: C
Question: The successive discounts 20% and 15% are equal to a single discount of?
A.43%
B.72%
C.32%
D.44%
Answer: C.32%
Explanation: C
32%
Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
Question: A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $1.80, what total number of pens and pencils did the customer purchase?
A.6
B.9
C.10
D.11
Answer: A.6
Explanation: Answer: Algebraically, the question looks like this: 2.5 = 0.35x + 0.25y There are three possible numbers of pens that fit that requirement:
1 pen: $0.35
2 pens: $0.70
3 pens: $1.05 and 3 pencils for $0.25 each. That's 3 pens and 3 pencils for a total of 6 pens and pencils. Choice (A) is correct.
Question: A reduction of 20% in the price of oil enables a house wife to obtain 4kgs more for Rs.600, what is the reduced price for kg?
A.20
B.40
C.36
D.30
Answer: D.30
Explanation: 600*(20/100) = 120 ---- 4
? ---- 1 => Rs.30
Answer:D
Question: Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 11 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?
A.37.5 kilometers per hour
B.48 kilometers per hour
C.49.2 kilometers per hour
D.75 kilometers per hour
Answer: C.49.2 kilometers per hour
Explanation: Time taken to reach first 40 km is 40/60 = 2/3 hr
Time taken to reach next 40 km is 40/60 = 2/3 hr
Time taken to reach next 20 km is 20/60 = 1/3 hr
Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...
Each stop was of 11 min , so two 11min break = 2*11/60 => 11/30 hr
Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+11/30 ) = 61/30 hrs
So, Average speed is 100/(61/30) = 49.2km/hour
Answer will be (C)
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
A.12
B.16
C.24
D.48
Answer: D.48
Explanation: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
Answer: Option D
Question: The product of a and b is equal to 11 more than twice the sum of a and b. If b = 5, what is the value of b - a?
A.-2
B.5
C.7
D.24
Answer: A.-2
Explanation: ab= 11 + 2(a+b)
5a= 11+2a +10
3a= 21
a=7
b-a= 5-7=-2
A is the answer
Question: 3 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2candidates. In how many ways can one cast his vote?
A.8
B.10
C.15
D.17
Answer: C.15
Explanation: There are 6 candidates and a voter has to vote for any two of them.
So, the required number of ways is,
= 6C2 = 6!/2!*4!
= 15.
C
Question: For which of the following values of n is (500+n)/n NOT an integer?
A. 1
B. 2
C. 3
D. 4
Answer: C. 3
Explanation: Solution:
This problem is easiest solved by plugging in each answer choice.
A) (500 + 1)/1 = 501/1 = 501
Answer choice A yields an integer.
B) (500 + 2)/2 = 502/2 = 251
Answer choice B yields an integer.
C) (500 + 3)/3 = 503/3 = 167, remainder 2
Answer choice C DOES NOT yield an integer.
Although we believe answer choice C is correct, we should still test the other answer choices.
D) (500 + 4)/4 = 504/4 = 126
Answer choice D yields an integer.
E) (500 + 5)/5 = 505/5 = 101
Answer choice E yields an integer.
Thus, the correct answer is answer choice C.
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
A.20
B.40
C.50
D.60
Answer: A.20
Explanation: Let the numbers be a, b and C. Then,
a2 + b2 + c2 = 138 and (ab + bc + ca) = 131
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
138 + 2 * 131 = 400
(a + b + c) = âˆš400 = 20
ANSWER A
Question: Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
A.5 : 7 : 8
B.20 : 49 : 64
C.38 : 28 : 21
D.30 : 20 : 15
Answer: B.20 : 49 : 64
Explanation: Explanation:
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,	14x	/8Y=5/7 =>98x = 40y =>y =	49/20X
And,	14x /7Z =5/8 => 112X=35Z=>z =	112/35 X 16/5X
x : y : z = x :49/20 X 16/5X =20 : 49 : 64.
ANSWER IS B
Question: When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 10 and the remainder is 3. What is the value of N?
A.151
B.331
C.511
D.43
Answer: D.43
Explanation: N/P=18 7/P= 18P+7
N/(P+2)=10 1/(P+2)=10P+20+3
solving these two equations
we get P=2 N= 43 answer is D
Question: Gary’s Gas Station serves an average of 13 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?
A.1,088
B.1,200
C.1,240
D.1,280
Answer: A.1,088
Explanation: 6 a.m. to 10 p.m. = 16 hours
Number of cars serviced on weekdays = (16 * 9 * 5)
Number of cars serviced on Saturday = (16 * 13)
Number of cars serviced on Sunday = (16 * 10)
Number of cars served in a week = 16(45 + 13 + 10) = 16 * 68 = 1088
Answer: A
Question: There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
A.A)3/7
B.B)5/8
C.C)6
D.D)5/6
Answer: D.D)5/6
Explanation: Let the two numbers be x and y.
30/100 * x + y = 5/4y
=> 3/10 x = 1/4 y => x/y = 5/6
D)
Question: If two sides of a triangle have lengths 6 and 8, which of the following could be the perimeter of the triangle? I. 9 II. 16 III. 19
A.None
B.I only
C.II only
D.III only
Answer: D.III only
Explanation: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Therefore:
(8-6) < {third side} < (8+6).
2 < {third side} < 14.
Perimeter = {third side} + 8 + 6 = {third side} + 14.
16 < {perimeter} < 28.
answer D
Question: If the sum of 6 consecutive integers is x, which of the following must be true?
I. x is a multiple of 6
II. x is an odd number
III. x is aneven number
A. I only
B. II only
C. III only
D. I and III
Answer: A. I only
Explanation: III. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
I. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 6p + 12 = 6 (p+2) => divisible by 6. There this must be true in all cases.
Therefore A is the answer.
Question: How many positive integers between 1 and 300 are there such that they are multiples of 21?
A.14
B.16
C.17
D.13
Answer: A.14
Explanation: Multiples of 21 = 21,42,63,-----294
Number of multiples of 21 => 21*14= 294
Answer is A
Question: 100 students appeared in 2 tests.60 students passed 1st test. 40 students passed in the 2nd test. 20 students passed in both 1 and 2 tests. what is the probability of the students who failed in both tests?
A.10%
B.15%
C.20%
D.25%
Answer: C.20%
Explanation: 20 student passed both two test
40 student passed only 1st test
20 student passed only 2nd test
so 100-(20+40+20)=20 student failed in both sub
so ans is 20%
ANSWER:C
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
A.11
B.12
C.18
D.77
Answer: C.18
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.Answer: C
Question: (12345679 x 72) = ?
A.777777777
B.888888888
C.666666666
D.999999999
Answer: B.888888888
Explanation: B
888888888
12345679 x 72 = 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888
Question: You collect baseball cards. Suppose you start out with 13. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
A.15
B.18
C.19
D.20
Answer: A.15
Explanation: Solution
Start with 13 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 13 + 1 which is 7,
so you're left with 13 - 7 = 6.
Peter takes 1 baseball card from you: 6 - 1 = 5 baseball cards.
Paul triples the number of baseball cards you have: 5 Ã— 3 = 15 baseball cards.
So you have 15 at the end.
Correct answer : A
Question: The difference between simple interest and C.I. at the same rate for Rs.5000 for 2 years in Rs.72. The rate of interest is?
A.12
B.17
C.18
D.16
Answer: B.17
Explanation: 5000 = 72(100/R)2
5 R2 = 720 => R = 12
Answer: B
Question: A large research project was scheduled over the course of a 30-month period, and a budget of $84,000 was allotted for the course of the entire project. After seven months, the project had spent $19,800. Was the project at this point over budget or under budget, and by how much?
A.under, $4200
B.0ver, $200
C.under, $700
D.over $1800
Answer: B.0ver, $200
Explanation: cost per month = 84,000/30 = 2,800.
Now, multiply by seven months: 7*($2800) = $19,600. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is more than this, so it is over budget.
$19,600 â€“ #19,800 = -$200
Answer = (B)
Question: In a certain Parallelogram the degree measure of one angle exceeds that of the other by 10 what is the degree measure of the smaller angle?
A.75
B.80
C.85
D.90
Answer: C.85
Explanation: In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).
Given: x+(x+10)=180 --> x=85.
Answer: C.
Question: The speed of a boat in upstream is 80 kmph and the speed of the boat downstream is 128 kmph. Find the speed of the boat in still water and the speed of the stream?
A.24
B.99
C.88
D.66
Answer: A.24
Explanation: Speed of the boat in still water = (80+128)/2 = 104 kmph. Speed of the stream = (80-60)/2 = 24 kmph. Answer:A
Question: In how many seconds will a train 180 meters long pass an oak tree, if the speed of the train is 36 km/hr?
A.14
B.16
C.18
D.20
Answer: C.18
Explanation: speed = 36 * 5/18 = 10 m/s
time = 180/10 = 18 seconds
The answer is C.
Question: An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.18522/- in 3 years at the same rate of interest. Find the rate percentage?
A.5%
B.7%
C.9%
D.11%
Answer: A.5%
Explanation: Explanation:
The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.
S.I = 18522/- - 17640/- = Rs. 882/-
Rate of interest = (882/17640) × (100/1) => 8820/1764 = 5%
Principal = Amount/(1 + R/100)2
= 17640/(1 + 5/100)2
= 17640/(21/20 × 21/20)
= 17640/(1.05 × 1.05)
= 17640/1.1025
= 16000
Thus the principal is Rs.16000/- and the rate of interest is 5%
Answer: Option A
Question: In how many ways can the letters of the word "CORPORATION" be arranged so that vowels always come together.
A.5760
B.50400
C.2880
D.None of above
Answer: B.50400
Explanation: Explanation:
Vowels in the word "CORPORATION" are O,O,A,I,O
Lets make it as CRPRTN(OOAIO)
This has 7 lettes, where R is twice so value = 7!/2!
= 2520
Vowel O is 3 times, so vowels can be arranged = 5!/3!
= 20
Total number of words = 2520 * 20 = 50400
Option B
Question: If three distinct positive divisors of 128 are randomly selected, what is the probability that their sum will be less than 32?
A.2/7
B.3/14
C.5/28
D.9/56
Answer: C.5/28
Explanation: The positive divisors are 1, 2, 4, 8, 16, 32, 64, 128.
If any of the first five are chosen, the sum will be less than 32.
P(sum is less than 32) = 5/8 * 4/7 * 3/6 = 60/336 = 5/28
The answer is C.
Question: An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.30 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?
A.700,000
B.300,000
C.380,000
D.400,000
Answer: A.700,000
Explanation: Total royalties for first 100.000 books = .8*100,000= 80,000
Total royalties for the rest of the books = 260,000-80,000 = 180,000
Remaining books = 180,000/0.3 = 600,000
Total books = 600,000+100,000 = 700,000 Answer A
Question: The average age of a class of 15 students is 10 years. If the age of the teacher be included, then the average increased by 1year. Find the age of the teacher?
A.22
B.23
C.26
D.29
Answer: C.26
Explanation: Total age of 15 persons = 15*10 = 150 years
Average age of 16 persons = 11years
Total age of 16 persons = 16 * 11 = 176 years
Age of the teacher = 176-150 = 26 years
Answer is C
Question: Jerome anticipated that the WebWeb.com stock price would fall and sold all his WebWeb.com stocks for $5 per stock. He paid $10,000 tax on the revenue. A week later, Jerome became convinced that the WebWeb.com stock price would rise, and he used the money that he had gotten from selling the WebWeb.com stocks to purchase them again, this time at $6 per stock. If Jerome ended up having 4000 WebWeb.com stocks fewer than the number he had before selling them, how many WebWeb.com stocks did he have originally?
A.10,000
B.11,600
C.12,000
D.14,000
Answer: D.14,000
Explanation: Let the number of shares be x.
5*x -10000(money paid in taxes) = 6(x- 4000)
Solving for x, we get the shares as 14000.
Ans :(Option D)
Question: What is the greatest prime factor of (13!12!) + (13!14!)?
.
A.11
B.13
C.47
D.61
Answer: D.61
Explanation: 13!12! + 13!14!
= 13!12! + 13! * 14 * 13 * 12!
= 13!12!(1 + 169+13)
= 13! 12! * 61 * 3
GCD = 61
Answer = D = 61
Question: For a race a distance of 224 meters can be covered by P in 7 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
A.800m
B.838m
C.834m
D.831m
Answer: A.800m
Explanation: Explanation:
This is a simple speed time problem. Given conditions:
=>Speed of P= 224/7 = 32m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken =25 seconds
Therefore, Distance covered by P in that time= 32m/s x 25 seconds = 800 metres
ANSWER: A
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players.
A.1745
B.1230
C.1365
D.2410
Answer: C.1365
Explanation: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
Ans: C
Question: John bought 9.25m of cloth for $425.50. Find the cost price per metre.
A.46
B.47
C.58
D.56
Answer: A.46
Explanation: Cloth bought by John = 9.25 m
Cost of 9.25 m = $425.50
Cost per metre = 425.50 ÷ 9.25
The cost of the cloth per metre = $ 46
Answers: A
Question: On my sister's birthday, she was 143 cm in height, having grown 10% since the year before. How tall was she the previous year?
A.140 cm
B.136 cm
C.130 cm
D.127 cm
Answer: C.130 cm
Explanation: Let the previous year's height be x.
1.1x = 143
x = 130
The answer is C.
Question: A goods train runs at the speed of 72 kmph and crosses a 350 m long platform in 26 seconds. What is the length of the goods train?
A.230 m
B.140 m
C.160 m
D.170 m
Answer: D.170 m
Explanation: Explanation:
Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,[ (x+350)/26 ]= 20
=> x + 350 = 520
=> x = 170. Answer: D