question stringlengths 3 1.14k | options listlengths 5 5 | rationale stringlengths 1 3.68k | correct stringclasses 5
values | cls int64 1 10 |
|---|---|---|---|---|
There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.? | [
"A)r / (r + b + w)",
"B)r * (r + b + w)",
"C)(r + b + w)",
"D)r / (r + b )",
"E)r / (b + w)"
] | The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A | A | 4 |
From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 9, what is the probability that the 2 numbers included the number 5? | [
"A)1/2",
"B)2/5",
"C)3/10",
"D)3/5",
"E)1/4"
] | We know that the sum of two numbers picked was 9. So, there could be the following cases:
(3, 6);
(6, 3);
(4, 5);
(5, 4);
Total of 4 cases out of which 2 have 5, thus the probability is 2/4=1/2.
Ans A | A | 1 |
Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4048. What is the difference between Rohan’s and Sudhir’s share in the profit? | [
"A)s.345",
"B)s.350",
"C)s.352",
"D)s.362",
"E)s.368"
] | Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 4048 × 1/11 = Rs.368.
E | E | 8 |
Find √? /20 = 4 ? | [
"A)76",
"B)6400",
"C)304",
"D)1296",
"E)None"
] | Answer
Let √N/20= 4
Then √N = 20 x 4 = 80
∴ N = 80 x 80= 6400.
Correct Option: B | B | 3 |
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 135 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage? | [
"A)8%",
"B)9%",
"C)11%",
"D)12.5%",
"E)14.8%"
] | Typical dosage is Dose : weight :: 2: 15.
Now if weight is 135 (Multiplying factor is 9: (135/15)) then typical dosage would be 2 *9 = 18cc.
Dosage = 18 cc. Dosage is greater by 2 cc.
% dosage is greater: (2 / 18)*100 = 11.11 %
C is the answer. | C | 4 |
A and B together can do a work in7 days. If A alone can do it in 14 days. In how many days can B alone do it? | [
"A)14",
"B)10",
"C)21",
"D)20",
"E)25"
] | A
14
1/7 – 1/14 = 1/14 => 14 | A | 8 |
If each edge of cube increased by 10%, the percentage increase in | [
"A)21",
"B)22",
"C)25",
"D)19",
"E)15"
] | 100 × (110)/100 × (110)/100 = 121 => 21%
Answer is A. | A | 6 |
A cistern has a leak which empty it in 8 hrs, A tap is turned on which admits 6 liters a minute into the cistern, and it is now emptied in 12 hours, How many liters does the cistern hold ? | [
"A)8640",
"B)8740",
"C)8840",
"D)8540",
"E)8940"
] | Inflow of water in 12hrs with rate 6 lit/min= 6*60*12= 4320
But, the same volume is emptied in 12 hrs, so the total capacity = total inflow + total outflow= 4320+4320= 8640
ANSWER:A | A | 8 |
A freight elevator can carry a maximum load of 1100 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between the... | [
"A)59",
"B)85",
"C)190",
"D)215",
"E)210"
] | The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1100 - 200 - 430 = 470.
allowed per package = 470 / 3 = 156
So difference in average of existing and allowable = 215 - 156 = 59
Hence A | A | 4 |
What is the area of a square field whose diagonal of length 20 m? | [
"A)150",
"B)300",
"C)200",
"D)450",
"E)600"
] | Explanation:
d^2/2 = (20 * 20)/2 = 200
Answer: C | C | 6 |
A family consists of two grandparents, two parents, and four grandchildren. The average age of the grandparents is 66 years, the average age of the parents is 40 years, and the average age of the grandchildren is 7 years. What is the average age (in years) of the family? | [
"A)26",
"B)28",
"C)30",
"D)32",
"E)34"
] | Total age of the grandparents = 66 × 2 = 132
Total age of the parents = 40 × 2 = 80
Total age of the grandchildren = 7 × 4 = 28
Average age of the family = (132+80+28)/8 = 240/8 = 30 years
The answer is C. | C | 5 |
What is the tens' digit T of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...? | [
"A)T=2",
"B)T=3",
"C)4",
"D)8",
"E)9"
] | All of the first 40 terms have 1 at the units place.
Except the first term, the tens digit of all the remaining 39 terms is 1.
So now if you do the addition
1 1
1 1
. . .
. . .
. . .
1 1
0 1
3 0
Answer is B | B | 9 |
Which of the following is closest to 10^180 – 10^20 ? | [
"A)10^210",
"B)10^180",
"C)10^150",
"D)10^90",
"E)10^6"
] | 10^180 – 10^20
10^20 * (10^160 – 1)
as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^160 – 1) would remain as 10^160.
and 10^20 * 10^160 = 10^180. Answer is B. | B | 1 |
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees ... | [
"A)45 minutes",
"B)50 minutes",
"C)40 minutes",
"D)54 minutes",
"E)35 minutes"
] | As they arrived 12 minutes earlier than usual, they saved 12 minutes on round trip from home to station (home-station-home) --> 6 minutes in each direction (home-station) --> wife meets husband 6 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent wak... | D | 7 |
Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 4 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts? | [
"A)560",
"B)561",
"C)562",
"D)563",
"E)547"
] | Total price of 8 t-shirts= 8*526=4208
Total price of 5 t-shirts=4*505=2020
Total price of 4 t-shirts=4208-2020=2188
Average price of 3 t-shirts=2188/4=547
Correct option Answer:E | E | 4 |
When x is divided by 3, the quotient is y and the remainder is 1. When x is divided by 5, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z? | [
"A)4z/7 + 5",
"B)(7z + 5) / 6",
"C)(6z + 7) / 4",
"D)(5z + 5) / 3",
"E)(4z + 6) / 7"
] | When x is divided by 3, the quotient is y and the remainder is 1: x = 3y + 1.
When x is divided by 5, the quotient is z and the remainder is 6: x = 5z + 6.
Equate those two:
3y + 1 = 5z + 6;
y = (5z + 5)/3.
Answer: D. | D | 2 |
If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 4 miles? | [
"A)12/5",
"B)12/3",
"C)12/4",
"D)12/6",
"E)12/2"
] | 1 km is approxmately equal to 0.6 miles
So 4 km = 4*0.6 = 2.4 miles . Multiple & divide by 10
i.e 2.4*10/10 = 24/10 = 12/5
Answer : A | A | 4 |
John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase? | [
"A)16%",
"B)16.66%",
"C)17.8%",
"D)18%",
"E)19.5%"
] | Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B | B | 4 |
A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: | [
"A)95",
"B)50",
"C)12",
"D)13",
"E)67"
] | Speed of the train relative to man = (250/10) m/sec = (25) m/sec. [(25) * (18/5)] km/hr = 90 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr.
Answer: Option A | A | 7 |
By how much is 3/5th of 875 greater than 2/3 of 333? | [
"A)239",
"B)303",
"C)288",
"D)127",
"E)191"
] | Explanation:
3/5th of 875 is greater than 2/3rd of 333
= 3/5 * 875 - 2/3 * 333
= 525 - 222 = 303.
Answer: B | B | 4 |
John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is? | [
"A)50",
"B)60",
"C)75",
"D)80",
"E)85"
] | (x+x1+...x14)/15 = 40
50
Option A | A | 5 |
How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/3!? | [
"A)1",
"B)3",
"C)5",
"D)6",
"E)0"
] | 3! =6
1/10 < 1/6 < 1
0.01 < 1/6 < 1
So 1/6 has 0 leading zeros
Answer: E | E | 3 |
If 4 men working 10 hours a day earn Rs. 1600 per week, then 9 men working 6 hours a day will earn how much per week? | [
"A)Rs 840",
"B)Rs 1320",
"C)Rs 1620",
"D)Rs 2160",
"E)None of these"
] | Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 1600 : x
hence 4 * 10 *x = 9 * 6 * 1600
or x = 9*6*1600/ 4*10 = 2160
Answer : D | D | 4 |
I flew my tiny seaplane to visit my mother. On the flight up, I flew at 140 mph. On the way home, I flew 88 mph. What was my average speed for the trip? | [
"A)114 mph",
"B)110 mph",
"C)88 mph",
"D)100 mph",
"E)99 mph"
] | (140 mph +88 mph)/2= 114 mph
Correct answer is: A | A | 7 |
(169)^2 - (168)^2 = | [
"A)1",
"B)100",
"C)229",
"D)329",
"E)337"
] | Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 168*2 + 1
= 336+1 = 337 = Answer = E | E | 3 |
If a and b are odd integers, which of the following is an even integer? | [
"A)3(2a+b)",
"B)3(2a+b)+2a",
"C)3(2a+b)+a+b",
"D)3(2a+b)+7a-b",
"E)3(2a+b)+ab"
] | 3(2a+b)+ab=odd(odd)+odd=odd+odd=even
The answer is E. | E | 2 |
√7 percent of 7√7 = | [
"A)0.55",
"B)0.96",
"C)0.1",
"D)0.45",
"E)0.6"
] | The other solutions are great, but here's one more approach.
First, we scan the answer choices to see that they are quite spread apart. This means we can also use someAPPROXIMATION
All test-takers must memorize the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
√6 ≈ 2.4
√7 ≈ 2.6
So, √7 percent of 7√7 ≈ 2.6 percen... | D | 4 |
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: | [
"A)100",
"B)110",
"C)120",
"D)130",
"E)150"
] | Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: Option D | D | 7 |
Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ? | [
"A)Rs. 4, Rs. 23",
"B)Rs. 13, Rs. 17",
"C)Rs. 15, Rs. 14",
"D)Rs. 17, Rs. 13",
"E)Rs. 19, Rs. 15"
] | Explanation:
Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.
Then, 2x + 3y = 77 ...(i) and
3x + 2y = 73 ...(ii)
Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.
Putting y = 17 in (i), we get: x = 13.
ANSWER IS B | B | 3 |
What is the HCF of 2/3, 4/9 and 6/5 | [
"A)7/45",
"B)2/45",
"C)4/15",
"D)8/45",
"E)9/45"
] | Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 9, 5) = 2/45
Answer: Option B | B | 2 |
Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 40% of the previous term. What is the value range of the five numbers? | [
"A)9,375",
"B)9,744",
"C)9,975",
"D)9,984",
"E)10,736"
] | 1st number= 10,000
2nd number = 40% of 10,000= 4000
3rd number= 40% of 4000= 1600
4th number = 40% of 1600= 640
5th number= 40% of 640= 256
Range = 10,000-256= 9744
B is the answer | B | 9 |
A number when divided by 5, gives 45 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 10 | [
"A)A)5",
"B)B)3",
"C)C)4",
"D)D)6",
"E)E)7"
] | Explanation:
P ÷ 5 = 45
=> P = 45 * 5 = 225
P / 10 =225 / 10 = 22, remainder = 5
Answer: Option A | A | 2 |
The sum of three integers A, B and C is 300. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C? | [
"A)175",
"B)180",
"C)185",
"D)190",
"E)195"
] | A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=300
so 1/3(B+C)+B+C=300
4(B+C)/3= 300
B+C =300*3/4 = 225
A=300-225=75
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=300
so 1/5(A+C)+A+C=300
A+C=300*5/6=250
but A=75, so C=250-75=175
Answer : A | A | 3 |
If A is thrice as fast as B and together can do a work in 15 days. In how many days A alone can do the work? | [
"A)36",
"B)20",
"C)28",
"D)54",
"E)45"
] | A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/15
= 3+1/3x = 4/3x = 1/15
x = 15*4/3 = 20
ANSWER:B | B | 3 |
If x^2=2x+2, then x^3 = ? | [
"A)3x+2",
"B)4x-2",
"C)2x+1",
"D)2x-3",
"E)6x+4"
] | x^2 = 2x+2
x^3 = x*x^2 = x*(2x+2) = 2x^2 + 2x = 2(2x+2)+2x = 6x+4
The answer is E. | E | 3 |
A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 9.00 a.m., at what time will he first touch a flag at 120 feet from the ground? | [
"A)4 p.m.",
"B)5 p.m.",
"C)6 p.m.",
"D)7 p.m.",
"E)None of these"
] | Explanation:
Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet.
So, the monkey ascends 90 feet in 9 hours i.e. till 6 p.m.
Clearly, in the next 1 hour i.e. till 7 p.m. the monkey ascends remaining 30 feet to touch the flag.
Answer:D | D | 7 |
In how many ways Chief Minister and Minister be elected from a team of 15 members? | [
"A)124",
"B)131",
"C)132",
"D)210",
"E)220"
] | To do this, if captain is elected first, then we have 15 ways of doing this.
For election of vice-captain, we have only 14 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 14*15 = 210 ways.
D | D | 3 |
Average weight of 10 people increased by 2.5 kg when one person of 45 kg is replaced by a new
man. Then weight of the new man is | [
"A)50",
"B)55",
"C)60",
"D)65",
"E)70"
] | Explanation:
Total weight increased is 2.5 * 10 = 25.
So weight of new person is 45+25 = 70
Answer: Option E | E | 5 |
A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 25 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/... | [
"A)8250",
"B)9350",
"C)10,450",
"D)11,550",
"E)12,650"
] | The distance the sound traveled to the man is 25*330 = 8250 meters
The answer is A. | A | 7 |
The diagonals of a rhombus are 12 cm and 20 cm. Find its area? | [
"A)176",
"B)186",
"C)120",
"D)179",
"E)172"
] | 1/2 * 12 * 20
= 120
Answer:C | C | 6 |
The sum of two consecutive integers is 31. Find the numbers. | [
"A)17, 18",
"B)7, 8",
"C)15, 16",
"D)1, 2",
"E)8, 9"
] | n + (n + 1) = 31
2n + 1 = 31
2n = 30
n = 15
Answer: C | C | 3 |
The sum of five numbers is 800. The average of the first two numbers is 100 and the third number is 150. Find the average of the two numbers? | [
"A)225",
"B)250",
"C)240",
"D)260",
"E)270"
] | Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 800
(P + Q)/2 = 100 and R = 150
P + Q = 200 and R = 150
P + Q + R = 350
S + T = 800 - (P + Q + R) = 450
Average of the last two numbers
= (S + T)/2 = 225
Answer:A | A | 3 |
Machine A working alone can complete a job in 10 hours. Machine A+B working alone can do the same job in 16 hours. How long will it take machine B working at their respective constant rates to complete the job? | [
"A)20/3",
"B)80/3",
"C)50/4",
"D)90/11",
"E)23/7"
] | Machines ( A ) ( B ) (A+B)
---Time - 10 - ( - ) -(16)
---Rate 16--- 6 -- 10
--Work 160 --160 -160
A+B = (160/6) = 80/3
B | B | 8 |
Sum of the squares of three numbers is 522 and the sum of their products taken two at a time is 131. Find the sum? | [
"A)20",
"B)22",
"C)25",
"D)27",
"E)28"
] | (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 522 + 2* 131
a + b + c = √784 = 28
E | E | 3 |
While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 6 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process... | [
"A)3",
"B)3.5",
"C)4",
"D)4.5",
"E)5"
] | Both computers together process files at a rate of 240/12 + 240/6 = 20+40 = 60 files per hour.
The time required to process 240 files is 240/60 = 4 hours
The answer is C. | C | 3 |
Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank? | [
"A)399",
"B)540",
"C)772",
"D)272",
"E)121"
] | 1/12 + 1/15 - 1/x = 1/15
x = 12
12 * 45 = 540
Answer: B | B | 8 |
In My, Xiang sold 15 used cars. For these 15 used cars the range of selling prices was 15,000 and the lowest selling price was 4,500. In June, Xiang sold 10 cars. For these 10 cars the range of selling was 16,000 and the lowest selling price was 5,000. What was the range of selling prices for the 25 used car sold by xi... | [
"A)15,600",
"B)15,750",
"C)16,820",
"D)18,100",
"E)19,200"
] | for 10 cars - 16000+ 5000 = 21,000
for 15 cars - 15000+ 4500 = 19,500
max = 21,000 min 4500
answer is approx 16,500.
Option C is closest. | C | 5 |
Six unbiased coin are tossed. What is the probability of getting atmost
one head? | [
"A)61/2",
"B)61/4",
"C)63/64",
"D)63/5",
"E)61/6"
] | Here n(S)= 2^6
Let E=event of getting atmost one head =
n(E)= 63
P(E)=n(E)/n(S)=63/64
Answer option C) | C | 1 |
A fruit seller had some apples. He sells 60% apples and still has 300 apples. Originally, he had: | [
"A)656 apples",
"B)700 apples",
"C)750 apples",
"D)780 apples",
"E)800 apples"
] | A fruit seller had some apples. He sells 60% apples and still has 300 apples. Originally, he had:
A.
656 apples
B.
700 apples
C.
750 apples
D.
780 apples
800 apples
Answer: Option D
Explanation:
Suppose originally he had x apples.
Then, (100 - 60)% of x = 300.
40/100 x x = 300
100
x = (300 x 1000)/40 = 750.
ANSWER :C | C | 4 |
Which of the following fractions is the largest? | [
"A)7/8",
"B)7/7",
"C)7/2",
"D)7/5",
"E)7/6"
] | L.C.M of 8, 16, 40 and 80 = 80.
7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80
Since, 70/80 > 63/80 > 65/80 > 62/80,
So, 7/8 > 63/80 > 13/16 > 31/40
So, 7/8 is the largest.
Answer: A | A | 4 |
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in: | [
"A)3 9 /17 hours",
"B)1 13 /17 hours",
"C)2 8 /11 hours",
"D)4 1 /2 hours",
"E)None of these"
] | Explanation:
Solution 1
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour =1/5
part filled by pipe B in 1 hour =1/6
Pipe C can empty the tank in 12 hours. Therefore,
part emptied by pipe C in 1 hour =1/12
Net part filled by Pipes A,B,C together in 1 hour =1/5 +1/6... | A | 8 |
Two tailors P and Q are paid a total of Rs. 550 per week by their employer. If P is paid 120 percent of the sum paid to Q, how much is Q paid per week? | [
"A)200",
"B)300",
"C)150",
"D)100",
"E)250"
] | Consider x
x+120 Of x =550
11/5x=550
x=550*5/11 = 250
ANSWER E | E | 4 |
A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 48 now, the son age 5 years back was | [
"A)14",
"B)17",
"C)11",
"D)19",
"E)99"
] | Let the son's present age be x years .Then, (48 - x) = x x= 24.
Son's age 5 years back = (24 - 5) = 19 years
Answer: D | D | 7 |
If 5a + 7b = g, where a and b are positive integers, what is the largest possible value of g for which exactly one pair of integers (a, b) makes the equation true? | [
"A)35",
"B)48",
"C)69",
"D)70",
"E)74"
] | 5*a1 + 7*b1 = g
5*a2 + 7*b2 = g
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding ... | D | 9 |
Which of the following must be subtracted from 2^24 so that the resulting integer will be a multiple of 3? | [
"A)2",
"B)3",
"C)1",
"D)4",
"E)5"
] | {4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : C | C | 3 |
How many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long | [
"A)30",
"B)40",
"C)50",
"D)60",
"E)70"
] | Explanation:
We need so simple divide 42.5/0.85,
=(4250/85) = 50
Option C | C | 4 |
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 188 cms. What was the ratio of men to women? | [
"A) 5:2",
"B) 5:1",
"C) 4:3",
"D) 5:4",
"E) 3:1"
] | We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 188cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 188M)/(W+M) = 180
170W + 188M = 180W + 180M
8M = 10W
4M = 5W
M/W =... | D | 5 |
Diesel costs Rs.4 per lit and petrol costs 7.23 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol. | [
"A)9 months",
"B)5 months",
"C)7 months",
"D)3 months",
"E)2 months"
] | Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324
=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85
=>In the fi... | C | 7 |
Apple costs X rupees per kilogram for first 30 kgs and Y rupees per kilogram for each additional kilogram. If the price of 40 kilograms is 420 and for 50 kgs of Apples is 540 then the cost of first 10 kgs of Apples is | [
"A)100",
"B)3.66",
"C)3.6",
"D)3.62",
"E)3.61"
] | Ans: By framing equations we get
30X+10Y=420
30X+20Y=540
Eliminate Q by multiplying the first equation by 2 and subtracting second equation from the first
60x+20y = 840 -
30x+20y = 540
=> 30x = 300 => x = 10
Then we get X = 10
Cost of 10 kgs of apples = 10x 10 = 100
Answer:A | A | 4 |
In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years replaced by a new boy. The age of the new boy is? | [
"A)14 years 8 months",
"B)15 years",
"C)16 years 4 months",
"D)17 years 10 months",
"E)17 years"
] | Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 18 years - 3 years 4 months.
= 14 years 8 months.
ANSWER:A | A | 8 |
If s and t are positive integers such that s/t = 64.28, which of the following could be the remainder when s is divided by t? | [
"A)12",
"B)15",
"C)18",
"D)21",
"E)24"
] | 0.28 = 28/100 = 7/25
The remainder must be divisible by 7.
The answer is D. | D | 1 |
Priya bought a fish last week. She was going to measure it but realized that her ruler was not long enough. She was able to measure the head and discovered that it was 12cm long; she then measured the tail and found that it was the length of the head plus one third of the length of the body. If the body was the length ... | [
"A)58",
"B)45",
"C)72",
"D)63",
"E)36"
] | Let us take H=Length of the head
T=Length of the tail
B=length of the body
Given that H=12 cms.
T=H+1/3 B => T=12+1/3B
Let this be the first equation
B=H+T
substituting the value of H and T here we will get
B=12+12+1/3B
=> B=24+1/3B
Therefore,B=36 cm
Substituting this in T we get
T=12+1/3(36)
T=12+12 =24
So now that yo... | C | 9 |
A train passes a station platform in 28 seconds and a man standing on the platform in 10 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? | [
"A)270",
"B)277",
"C)240",
"D)88",
"E)112"
] | Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 10) m = 150 m.
Let the length of the platform be x meters.
Then, x + 150 / 28 = 15
x + 150 = 420
x = 270 m.
Answer:A | A | 7 |
Two partners in a business (Carol and Ben) invested $500 and $850 in a business respectively. At the end of the year they made a profit of $250. Find share of each partner? | [
"A)$92.59,$157.41",
"B)$96.59,$157.41",
"C)$92.59,$159.41",
"D)$92.59,$127.41",
"E)$12.59,$157.41"
] | A:B = 500:850
A:B = 10 : 17
A's share = 250*10/27 = $92.59
B's share = 250*17/27 = $157.41
Answer is A | A | 4 |
If four coins are tossed, the probability of getting two heads and two tails ? | [
"A)3/8",
"B)3/7",
"C)3/86",
"D)3/5",
"E)3/2"
] | Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A | A | 1 |
Find the one which does not belong to that group ? | [
"A)22",
"B)83",
"C)33",
"D)49",
"E)11"
] | Explanation:
36 = 62, 49 = 72, 64 = 82, 81 = 92 and 100 = 102.
36, 64, 81 and 100 are squares of composite numbers, but not 49.
Answer: B | B | 10 |
The product S of the first 10 prime numbers is closest to which of the following? | [
"A)6.5 x 10^7",
"B)6.5 x 10^8",
"C)6.5 x 10^9",
"D)6.5 x 10^10",
"E)6.5 x 10^11"
] | The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.
# of different approximations are possible. For example:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667=S
2*3*5... | C | 2 |
A person takes 5hrs 45 min in walking to a place and ridingback. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is? | [
"A)5 hours 45 min",
"B)5 hours 55 min",
"C)6 hours 45 min",
"D)7 hours 45 min",
"E)8 hours"
] | ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding ... | D | 8 |
If Tim had lunch at $50 and he gave 20% tip, how much did he spend? | [
"A)A)$60.00",
"B)B)$35.42",
"C)C)$60.60",
"D)D)$21.56",
"E)E)$78.45"
] | The tip is 20% of what he paid for lunch.
tip = 20% of 50.00 = (20/100)*50.00 = = $10.00
Total spent
50.00 + 10.00 = $60.00
correct answer is A)$60.00 | A | 4 |
A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks white,yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebooks are pu... | [
"A)1/49",
"B)1/8",
"C)1/7",
"D)2/7",
"E)1/2"
] | After white,yellow, orange, green, red, blue, and purple, the next book can be of any given seven colours, therefore we have total seven possibilities, out of which we need purple i.e. 1 therefore prob is 1/7
Answer:C | C | 1 |
X can lay railway track between two station in 16; Y can do the same work in 20 days,both are working together for 2 days after Y left the job then how many days X requires to complete the remaining work ? Total number of days taken to complete the whole work? | [
"A)7 Days and 9 days",
"B)5.89 Days and 7.89 days",
"C)8.26 Days and 10.26 days",
"D)7.75 Days and 9.75 days",
"E)9 Days and 11 days"
] | First take LCM of (16,20) = 160; Total work = 160; X's one day work = 160/16 =10; Y's one day work =160/20 = 8; One day work of both X+Y= 10+8 = 18; Total work completed in 2 days = 18*2=36; remaining work is = 160 - 36 =124; remaining work completed by X in = 124/16= 7.75 days.Total number of days taken to complete th... | D | 8 |
A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 3.5 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? | [
"A)3",
"B)4.2",
"C)3.4",
"D)5.5",
"E)5.7"
] | 72 km/hr = 1.2 km/min
The total distance is 3.6 km.
3.6 / 1.2 = 3 minutes
The answer is A. | A | 7 |
For all even numbers n, h(n) is defined to be the sum of the even numbers between 4 and n, inclusive. What is the value of h(12)/h(10) ? | [
"A) 1.8",
"B) 3",
"C) 6",
"D) 1.5",
"E) 60"
] | CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then
Mean = Median =(First+Last)/2
and Sum = Mean*Number of terms
h(12) = [(4+12)/2]*5 = 40
h(10) = (4+10)/2]*4 = 28
h(12)/h(10) = (40) / (28) ~ 1.5
Answer : D | D | 3 |
The smallest number which when diminished by 3 is divisible by 21,28,36 and 45 is... | [
"A)829",
"B)869",
"C)859",
"D)4320",
"E)427"
] | 427
ANSWER:E | E | 2 |
A boy has Rs. 560 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? | [
"A)90",
"B)105",
"C)140",
"D)130",
"E)120"
] | Let number of notes of each denomination be x.
Then x + 5x + 10x = 560
16x = 560
x = 35.
Hence, total number of notes = 3x = 105.
B | B | 3 |
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? | [
"A)87 cm2",
"B)28 cm2",
"C)98 cm2",
"D)26 cm2",
"E)35 cm2"
] | 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 * 28/2
= 35 cm2
Answer:E | E | 6 |
At what rate percent on simple interest will Rs.1800 amount to Rs.2000 in 5 years? | [
"A)4 %",
"B)3 6/7 %",
"C)2 6/7 %",
"D)3.47%",
"E)6 %"
] | Explanation:
250 = (1800x5xR)/100
R = 3.47%
Answer: Option D | D | 3 |
5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is? | [
"A)1:2",
"B)2:1",
"C)2:3",
"D)6:5",
"E)3:1"
] | Explanation:
5Men + 12Boys ----- 4 days
7Men + 6Boys ------- 5 days
20Men + 48Boys = 35Men + 30Boys
18Boys = 15Men => 5Men = 6Boys
Men : Boys = 6:5
Answer: D | D | 8 |
How long does a train 165 meters long running at the rate of 36 kmph take to cross a bridge 660 meters in length? | [
"A)33",
"B)72",
"C)55",
"D)82.5",
"E)62"
] | Explanation:
T = (660 + 165)/36 * 18/5
T = 82.5
Answer: Option D | D | 7 |
Ed throws a blue die and a red die. How many combinations are there in which the two dice do not yield the same result and the sum of the results is not 9? | [
"A)10",
"B)24",
"C)26",
"D)30",
"E)36"
] | Total number of combination is 6*6 = 36..
Condition 1: we shouldn't get the same number... (1,1)(2,2)(3,3)(4,4)(5,5)(6,6) - 6 combinations.
condition 2: We shouldn't get the 9 as the sum (4,5)(5,4)(3,6)(6,3) - 4 combinations...
Total = 36 - 10 = 26.
ANS option C. | C | 1 |
The volume of a cube is 729 cc. Find its surface. | [
"A)486",
"B)556",
"C)255",
"D)287",
"E)267"
] | a3 = 729 => a = 9
6a2 = 6 * 9 * 9 = 486
Answer:A | A | 6 |
The ratio, by volume, of soap to alcohol to water in a certain solution is 6:30:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 150 cubic centimeters of alcohol, how many cubic centimeters of water will it ... | [
"A)1200",
"B)1300",
"C)1500",
"D)1800",
"E)1900"
] | soap:alcohol
Initial ratio soap:alcohol: water --> 6:30:90
Initial soap:alcohol = 6/30 =6:30
after doubled soap:alcohol =2* 6/30 = 12/30=12:30
Initial soap:water = 6/90=6:90
after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360
After soap: alcohol:water --> 12:30:360
given alcohol 150 cubic centimeter.
ratio is 60:... | D | 4 |
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years? | [
"A)387",
"B)400",
"C)776",
"D)268",
"E)181"
] | 441 = P(21/20)2
P = 400
Answer:B | B | 3 |
Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? | [
"A)10 hours",
"B)17 hours",
"C)19 hours",
"D)16 hours",
"E)27 hours"
] | Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A | A | 8 |
A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? | [
"A)125786",
"B)158799",
"C)564323",
"D)344567",
"E)220030"
] | (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
E | E | 3 |
If a is the sum of u consecutive positive integers. b is the sum of v consecutive positive integers. For which of the following values of u and v is it impossible that a = b? | [
"A)u = 2; v = 6",
"B)u = 3; v = 6",
"C)u = 7; v = 9",
"D)u = 10; v = 7",
"E)u = 10; v = 4"
] | I approached this in a different way, although may be longer but it's certainly more intuitive
It is impossible that a = b if one of them is necessarily even while the other is necessarily odd
for two consecutive integers the sum is necessarily odd
for six consecutive integers the sum is necessarily odd (sum of 3two co... | E | 3 |
A certain high school has 500 students. Of these students, 30 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art? | [
"A)430",
"B)440",
"C)450",
"D)460",
"E)470"
] | We're given a series of facts to work with:
1) A certain high school has 500 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.
We're asked how many students are taking NEITHER music nor art?
Let's TEST
X = 30
Y = 20
Z = 10
So, we have 30 students taking music, 20... | D | 5 |
A sales executive receives an annual bonus if he meets a certain target. This year, the salesman has so far sold 1/4 of last year's quota. If this year's quota is reduced by 20 percent from last year, how much target percentage of this year's target does he still need to complete to get bonus? | [
"A)15/25",
"B)4/20",
"C)3/4",
"D)15/20",
"E)9/10"
] | We have 1/5 and 20% which is 1/5. Let's pick some smart numbers.
Assume last year's quota to be 25.
This year's quota = 20% reduction from 25 = 20
Sold so far = 1/5 * 25 = 5
Remaining = 20-5 = 15
Required = 15/25
Answer (A). | A | 7 |
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in... | [
"A)7",
"B)10",
"C)15",
"D)17",
"E)20"
] | If 6 colors have to be divided into groups of 2, the number of unique groupings 6C2 = 6! / (2!)(4!) = 15.
Number of combinations was sufficient to account for all but 5 of the subjects
Number of subjects = 15 + 5 = 20.
ANSWER:E | E | 3 |
Six years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages | [
"A)A)21",
"B)B)34",
"C)C)45",
"D)D)25",
"E)E)26"
] | Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Six years ago, P was half of Q in age
=> 2(3x – 6) = (4x – 6)
=> 6x – 12 = 4x – 6
=> 2x =6
=> x = 3
7x=7*3=21
Answer: Option A | A | 5 |
What is the value of 4^5+4^6? | [
"A) 5(4^5)",
"B) 4^35",
"C) 17(4^5)",
"D) 8^12",
"E) 7(4^5)"
] | 4^5+4^6
=4^5(1+4^1)
=4^5 * 5
Answer A | A | 3 |
In how many no. between 10 and 30 exactly Two of the digits is 2? | [
"A)25",
"B)1",
"C)35",
"D)45",
"E)50"
] | It's simple can be solved by elimination of answer choices.
Option A and C are too large, not possible. Even DE are large to have correct choice.
Ans : B | B | 9 |
The cost of cultivating a square field at the rate of Rs.135 per hectare is Rs.1215. The cost of putting a fence around it at the rate of 75 paise per meter would be : | [
"A)Rs.360",
"B)Rs.810",
"C)Rs.900",
"D)Rs.1800",
"E)Rs.1900"
] | Area= Total cost/ Rate= (1215/135) hectares= (9*10000) sq.m.
Therefore, side of the square= Ö90000=300m.
Perimeter of the field= (300*4)m= 1200m
Cost of fencing= Rs.(1200*3/4)= Rs.900
ANSWER:C | C | 4 |
If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 2? | [
"A)5/6",
"B)7/36",
"C)5/36",
"D)1/36",
"E)12/36"
] | The sum of numbers appeared is 2.
Therefore, the required probability = n(E)/n(S) = 1/36.
ANSWER:D | D | 1 |
The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 8 years ago, the sum of their ages was 76, what will be the age of Charlie 9 years from now? | [
"A)44",
"B)52",
"C)57",
"D)65",
"E)80"
] | Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.
5x-8 + 8x-8 + 7x-8 = 76
x = 5
Present age of Charlie = 7*5 = 35
Charlie's age 9 years hence = 35+9 = 44
Answer = A | A | 4 |
The closest approximation of W(69.28 × 0.004)/0.03 is | [
"A)0.092",
"B)0.92",
"C)9.2",
"D)92",
"E)920"
] | W(69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1... | C | 4 |
Two representatives must be selected from each of two groups of students. One group consists of three men and two woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ? | [
"A)1/6",
"B)1/4",
"C)2/7",
"D)1/3",
"E)5/12"
] | Group 1: 3 Men and 2 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 3C2*2C2 = 3 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*2*1*2 = 12 ways
Total Favorable cases = 3+12 = 15
Total Possible ways of selecting students 2... | E | 1 |
Which of these must the factor Q of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80 | [
"A)1,2 only",
"B)Q=2,3 only",
"C)Q=1,2,3 only",
"D)Q=1,2,3,4 only",
"E)All of them"
] | Let the four variables be a< b< c< d.
Assume a worst case scenario where the a equal to a prime number (hence odd).
therefore
a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)
therefore
each answer choice must be divisible Q by 2 x 3 x 4 = 24
only 80 is not divisible. T... | D | 1 |
The ages of Ashley and Mary are in the ratio 4:7. The sum of their ages is 22. Find the ages of Ashley . | [
"A)7",
"B)8",
"C)9",
"D)10",
"E)11"
] | a:m=4:7
let the ages of a & m be x &22-x
x/22-x=4/7
x=8
a=8yrs
ANSWER:B | B | 10 |
If a cistern has 3 pipes of 1 cm , 4/3 cm and 2 cm thickness ...where the pipe with 2 cm thickness can fill the cistern in 2 hrs and 2 min..then in how much time they can fill the tank? | [
"A)53.7min",
"B)54.7min",
"C)55.7min",
"D)56.7min",
"E)57.7min"
] | 2cm can fill in 122min
thickness inversly propotional to time
total thickness of the pipe=1+4/3+2=4.3
we know that 2cm can fill in 122min
for 4.3cm time =56.7min
ANSWER:D | D | 8 |
End of preview. Expand in Data Studio
Dataset Card for "aqua_rat_cls"
- Probability & Statistics • Includes classical and conditional probability, independent/mutually exclusive events • Permutations and combinations, sampling, expected value, variance, standard deviation • Normal distribution, central tendencies (mean, median, mode) Explanation: Focuses on quantifying uncertainty and data analysis, requiring both discrete counting and continuous distribution understanding.
⸻
- Number Theory & Integer Properties • Integer operations, parity (odd/even), primes and composites • Factors, multiples, GCD (Greatest Common Divisor), LCM (Least Common Multiple) • Modular arithmetic, remainders, digit-based problems Explanation: Emphasizes understanding the structure and properties of integers through factorization, divisibility, and modular relationships.
⸻
- Algebra & Equations • Linear equations (single/multi-variable), quadratic equations, root relationships • Polynomial and rational expressions, radicals, exponents, logarithms • Absolute value equations/inequalities, algebraic identities, functional equations Explanation: Involves constructing and solving symbolic representations of mathematical relationships, using transformations and manipulation.
⸻
- Ratios, Percentages & Proportion Applications • Ratio and proportion, allocation problems, mixture/concentration • Percentage increase/decrease, profit/loss, markup/discount • Rapid estimation and chain ratio calculations Explanation: Centers around understanding relative quantities and applying them to real-life scenarios involving finance, mixtures, and scaling.
⸻
- Averages & Data Analysis • Simple and weighted averages, mean adjustments • Impacts of adding/removing data on the mean • Graph/table interpretation (e.g., line graphs, bar charts) Explanation: Evaluates a student’s ability to compute, interpret, and manipulate averages in dynamic or tabulated datasets.
⸻
- Geometry & Measurement • Plane geometry: triangles, quadrilaterals, circles – perimeter, area • Solid geometry: prisms, cylinders, cones, spheres – volume, surface area • Coordinate geometry: slopes, distances, midpoints Explanation: Involves spatial reasoning and applying geometric formulas to compute dimensions, shapes, and their relationships.
⸻
- Time, Speed & Distance • Problems involving meeting/relative motion, chase scenarios • Average speed, train/bridge problems, circular tracks • Real-life travel and movement-based contexts Explanation: Centers around modeling physical motion using distance = speed × time, including multi-object interactions.
⸻
- Work & Rate Problems • Cooperative work (people/machines), remaining work • Pipes and cisterns, batching, alternate shifts • Inverse proportionality of rate and time Explanation: Applies the concept of work = rate × time, focusing on multi-agent collaboration and task completion efficiency.
⸻
- Sequences & Series • Arithmetic and geometric progressions (formulas, sums) • Recursive/defined sequences, Fibonacci, periodic or patterned sequences • Rule-based prediction and term computation Explanation: Trains pattern recognition and inductive reasoning through formulas or recursive definitions to identify terms and sums.
⸻
- Word Problems & Logical Reasoning • Real-world math: investment, profit-sharing, age, population changes • Set theory, inclusion-exclusion, seating arrangements, logical deduction • Multi-step, cross-topic problem-solving Explanation: Tests the ability to build models and reason through complex scenarios that integrate multiple math concepts or logical steps.
- Downloads last month
- 6