divelab/Sys2Bench huggingface dataset:
Question: In a group of 28 junior high school students, 7 take French, 9 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
Options:
A)7
B)6
C)9
D)4
E)8
Rationale: E
8
Add 7 + 9 + 4 to get 20.
Then subtract 21 from the total students ⇒ 28 – 20 = 8.
Answer is E
Answer: E
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 81. What is that number
Options:
A)9
B)10
C)12
D)14
E)15
Rationale: Explanation:
=> 3(2x+9) = 81
=> 2x+9 = 27
=> x = 9
Answer: Option A
Answer: A
Question: If 3 machines can build a car in 12 hours, how fast can 4 machines do it?
Options:
A)10 hours
B)9 hours
C)8 hours
D)7 hours
E)11 hours
Rationale: 3 * 12 = 4 * x
x = 9 hours
Answer: B
Answer: B
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Options:
A)27 7/9m
B)27 m
C)33 m
D)23 4/9 m
E)25 m
Rationale: Relative speed = (40 - 20) km/hr = ( 20 x 5/18 ) m/sec = 50/9 m/sec.
Therefore Length of faster train = ( 50/9 x 5 ) m = 250/9 m = 27 7/9 m.
ANSWER A
Answer: A
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)Rs.270
B)Rs.185
C)Rs.215
D)Rs.380
E)Rs.315
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
ANSWER:A
Answer: A
Question: A student completes a 3 part exam as follows. The student completes section A in 10 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?
Options:
A)5:2
B)4:1
C)4:3
D)3:2
E)2:1
Rationale: The time spent on section B and section C is 25 minutes each.
The ratio of C to A is 25:10 = 5:2
The answer is A.
Answer: A
Question: Two trains of length 100 m and 200 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?
Options:
A)80/9 sec
B)80/7 sec
C)30/7 sec
D)80/8 sec
E)81/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.Answer:B
Answer: B
Question: 10 Arabian horses are split into pairs to pull one of the distinct 4 carts in a race. If each cart is assigned to a pair, how many different assignments of horses to carts are possible?
Options:
A)420
B)1260
C)5220
D)9450
E)113400
Rationale: # of ways 10 horses can be divided into 5 groups when order of the groups does not matter is: C210∗C28∗C26∗C24∗C225!=945C102∗C82∗C62∗C42∗C225!=945.
So we would have 945 different cases of dividing 10 horses into 5 groups:
1. A1A1, B1B1, C1C1, D1D1, E1E1 (each letter represent pair of horses);
2. A2A2, B2B2, C2C2, D2D2, E2E2;
...
945. A945, B945, C945, D945, E945.
Now, we want to assign a pair (a letter in our case) to one of 4 distinct carts. For each case (out of 945) P45=120 would represent # of ways to choose 4 pairs out of 5 when order matters (as carts are distinct). OR C45 choose 4 different letters out of 5 and 4! - # of ways to assign 4 different letters to 4 distinct carts: C45∗4!=120C.
So total # of different assignments would be 945∗120=113400
Answer: E.
Answer: E
Question: The side of a square is increased by 25% then how much % does its area increases?
Options:
A)56.65 %
B)56.25 %
C)56.29 %
D)57.25 %
E)56.55 %
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer: B
Answer: B
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 1 hour?
Options:
A)100
B)120
C)150
D)180
E)240
Rationale: Answer = 4 * 60 = 240
Answer is E
Answer: E
Question: A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '1' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
Options:
A)65
B)60
C)50
D)70
E)80
Rationale: problem of combination 8C4 = 8!/4!*(8-4)! = 8*7*6*5*4!/4!*4! =70
D
Answer: D
Question: 3,8,18,38,78,__
Options:
A)158
B)156
C)154
D)150
E)148
Rationale: 8=3*2+2
18=8*2+2
38=18*2+2
78=38*2+2
158=78*2+2
ANSWER:A
Answer: A
Question: Two pipes A and B can separately fill a cistern in 60 minutes and 80 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 40 minutes. In how much time, the third pipe alone can empty the cistern?
Options:
A)90 min
B)100 min
C)240 min
D)120 min
E)130 min
Rationale: 1/40-(1/60+1/80)=-1/240
third pipe can empty in 240 minutes
ANSWER:C
Answer: C
Question: In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
Options:
A)1
B)2
C)3
D)6
E)7
Rationale: 23912/33333 = 0.71736
There is a pattern , the set of 5 digits keeps repeating , so we have a cyclic order....
98/5 = 19 complete cycles and 3 remainder...
3rd digit from the right will be 7
Hence, the correct answer will be (E) 7
Answer: E
Question: Find the surface area of a cuboid 16 m long, 8 m broad and 7 m high
Options:
A)868 sq.cm
B)920 sq.cm
C)727 sq.cm
D)832 sq.cm
E)None of these
Rationale: Explanation:
Surface area = [2 (16 x 8+ 8 x 7 + 16 x 7)] cm2 = (2 x 416)cm2 = 832 cm2.
Answer: D
Answer: D
Question: what is the smallest integer that is multiple of 7, 9 and 20
Options:
A)141
B)180
C)130
D)1260
E)1420
Rationale: Correct Answer :D
It is the lcm of 7, 9 and 20 which is 1260
Answer: D
Question: Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 14 candidates. She plans to have one working interview with 3 of the 14 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?
Options:
A)720
B)120
C)300
D)30
E)333
Rationale: 333.
Answer E
Answer: E
Question: complete the series..
2 2 12 12 30 30 ?
Options:
A)25
B)53
C)54
D)55
E)56
Rationale: it follows the series as:
1 * 2 = 2
2 * 1 = 2
3 * 4 = 12
4 * 3 = 12
5 * 6 = 30
6 * 5 = 30
7 * 8 = 56------> this is the required number for the series.
8 * 7 = 56.
ANSWER:E
Answer: E
Question: The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year. If the initial value of the scooter is Rs.40,000, what is the value at the end of 4 years ?
Options:
A)3277
B)2977
C)12656
D)6077
E)17112
Rationale: Explanation: 40,000*(3/4)^4
Answer:C
Answer: C
Question: A bus leaves Burbank at 9:00 a.m. traveling east at 50 miles per hour. At 1:00 p.m. a plane leaves Burbank traveling east at 300 miles per hour. At what time will the plane overtake the bus?
Options:
A)12:45 p.m.
B)1:10 p.m
C)1:40 p.m
D)1:48 p.m
E)1:55 p.m
Rationale: distance = speed * time
from 9:00 am to 1:00 pm total is 4 hrs
In 4 hrs bus travels a distance of 50 * 4 = 200 miles
plane starts travelling in same direction so relative speed = 300 - 50 = 250 miles/hr
distance the plane needs to cover so as to overtake the bus is 200 miles
time = 200 /250 = 4/5 hrs = 48 minutes
so at 1:48 pm the plane overtakes the bus
Correct answer - D
Answer: D
Question: If log 27 = 1.431, then the value of log 9 is:
Options:
A)0.934
B)0.945
C)0.954
D)0.958
E)0.998
Rationale: log 27 = 1.431
log (3cube ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(3square ) = 2 log 3 = (2 x 0.477) = 0.954.
Answer: Option C
Answer: C
Question: A, B and C are pipes attached to a cistern. A and B can fill it in 10 and 15 minutes respectively, While C can empty it in 20 minutes. If A, B and C be kept open successively for one minute each, find the last integral number of minutes required for the cistern to get filled
Options:
A)24 min 40 sec.
B)24 min 30 sec.
C)24 min 20 sec.
D)24 min 10 sec.
E)24 min 50 sec.
Rationale: 3 min filling=(1/10)+(1/15)-(1/20)=7/60
So upto 3*8=24th min, cistern filled=7*8/60=56/60=14/15
Remaining=1/15, which is to be filled by 'A' again
time taken by A=(1/15)/(1/10)=2/3 min.=40 sec.
So total time required=24 min+ 40 sec.
ANSWER:A
Answer: A
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Options:
A)16
B)24
C)25
D)96
E)28
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3
= 75.
In a game of 100 points, B gives (100 - 75)
= 25 points to C.
Answer: C
Answer: C
Question: There are 12 points marked on the circumference of a circle. How many hexagons can be formed by connecting 6 points of the 12 points?
Options:
A)908
B)912
C)916
D)920
E)924
Rationale: 12C6=924
The answer is E.
Answer: E
Question: A man invests in a 16% stock at 128. The interest obtained by him is :
Options:
A)12.9%
B)92.5%
C)12.5%
D)12.6%
E)12.7%
Rationale: Explanation:
By investing Rs 128, income derived = Rs. 16
By investing Rs. 100, income derived = = Rs.12.5
Interest obtained = 12.5%
Answer: C) Rs. 12.5%
Answer: C
Question: What approximate value will come in place of the question mark(?) in the following equation?
2070.50 ÷ 15.004 + 39.001 × (4.999)2 = ?
Options:
A)1005
B)997
C)1049
D)1213
E)1113
Rationale: 2070.50 ÷ 15.004 + 39.001 × (4.999)2 = ?
or? ≈ 2070 ÷ 15 + 39 × 5 × 5
= 138 + 975 = 1113
Answer E
Answer: E
Question: How many multiples of 7 are there between 9 and 89, 9 and 89 inclusive ?
Options:
A)11
B)17
C)16
D)13
E)12
Rationale: 7 multiples are ...14,21,28,35,42,49,56,63,70,77,84,
...
,...,
the answer is =11
Answer is A
Answer: A
Question: 33 1/3% OF 330?
Options:
A)80
B)90
C)110
D)120
E)130
Rationale: 33 1/3 % = 1/3
1/3 × 330 = 110
C)
Answer: C
Question: A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 998 ?
Options:
A)249
B)498
C)676
D)823
E)1,002
Rationale: slope of 2 and a y-intercept of 2
y-coordinate is 998
y = 2x + 2
996 = 2x
x = 498
Answer:
B. 498
Answer: B
Question: How many distinct integer values of n satisfy the inequality||n-3| + 4| ≤ 11?
Options:
A)15
B)16
C)17
D)8
E)19
Rationale: so i can write this as In-3I+4<=11
or In-3I<=7
so n can have -4 to 10 = 8 true values....
D
Answer: D
Question: In a soccer bet,we play 4 teams.first team odd 1.27,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?
Options:
A)219.5
B)221.26
C)235.01
D)266.74
E)669.0
Rationale: in the case we won the bet,we have:
1.27* 5.23* 3.25* 2.0*5.00=219.50
we will win 221.26
so correct answer is B
Answer: B
Question: The length of rectangle is thrice its breadth and its perimeter is 112 m, find the area of the rectangle?
Options:
A)432 sq m
B)356 sq m
C)452 sq m
D)588 sq m
E)525 sq m
Rationale: 2(3x + x) = 112
l = 42 b = 14
lb = 42 * 14 = 588
ANSWER:D
Answer: D
Question: The length of a rectangle is halved, while its breadth is tripled. Whatis the % change in area?
Options:
A)30%
B)40%
C)50percent
D)60%
E)70%
Rationale: Let original length = x and original breadth
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: C
Question: The diameter of a cylindrical tin is 14cm and height is 5 cm. Find the volume of the cylinder?
Options:
A)230
B)141
C)66
D)245
E)21
Rationale: r = 7 h = 5
π * 7 * 7 * 5 = 45 π cc
Answer:D
Answer: D
Question: List I: { y, 2, 4, 7, 10, 11}
List II: {3, 3, 4, 6, 7, 10}
If the median E of List I is equal to the sum of the median of list II and the mode of list II, then y equals
Options:
A)5
B)7
C)8
D)E=9
E)10
Rationale: mode of list ii =3
median E of list ii =4+6/2 =5
sum of mode + mean = 3+ 5=8
now to make 8 as the median we need to find a value of y such that if the no. of terms in list 1 are odd then y=8 else if even then 7+y /2=8
here its even so
7+y/2=8 from this y= 9 (D)
Answer: D
Question: In a Express Train passengers traveling in A.C. Sleeper Class, First Class and Sleeper Class are in the ratio 1:2:3, and fare to each class in the ratio 5:4:2. If the income from this train is Rs. 57000, the income of A.C. Sleeper Class is
Options:
A)Rs. 8000
B)Rs. 12000
C)Rs. 15000
D)Rs. 6000
E)None
Rationale: Income is divided in the ratio 1×5:2×4:3×2= 5:8:6.
Now 5x + 8x + 6x = 19x = 57000.
∴ x =3000.
Therefore income from A.C. Sleeper Class = 30005=15000.
Answer:C.
Answer: C
Question: A shopkeeper marks up the price of his goods by 20% and gives a discount of 10% to the customer. He also uses a 900g weight instead of 1Kg weight. Find his profit percentage.
Options:
A)8%
B)12%
C)20%
D)30%
E)None of these
Rationale: Let the C.P of 1000g of goods be Rs 1,000
Market price = Rs 1,200
Selling price = Rs 1,200 x 0.9 = Rs 1,080 (after discount of 10% )
If Rs 1080 is the selling price of 900g of goods ( as he cheats of 10 % while selling )
C.P of 900g = Rs 900
Profit = Rs 180
Therefore, Profit % = (180/900 ) x 100 = 20 %
ANSWER:C
Answer: C
Question: What is the difference between the largest and the smallest number written with 7, 7, 0, 7?
Options:
A)337
B)628
C)987
D)693
E)281
Rationale: Explanation:
7770
7077
-------------
693
Answer: D
Answer: D
Question: WHAT IS correct mathematical solution for the number of ways that the letters of the word BANANA could be arranged to create a six-letter code?
Options:
A)A)6!
B)− (3! + 2!)
C)− (3! × 2!)
D)+ 2!)
E)× 2!)
Rationale: Number of letters in word 'BANANA' = 6.
The letters 'A' and 'N' appear 3 times and 2 times respectively in the word 'BANANA'.
Therefore the mathematical solution for number of ways that the letters of the word BANANA can be arranged to create six-letter code
= 6!/(3!*2!)
Answer: E
Answer: E
Question: What is 15% of 2/3 of 0.6?
Options:
A)0.06
B)0.9
C)9
D)90
E)None of the above
Rationale: The best way to solve these questions is to convert every term into fraction
(15/100)*(2/3)*(6/10) = 180/3000 = 0.06
Option A
Answer: A
Question: In a garden, four are three blue flowers, four red flowers, four green flowers, and four pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?
Options:
A)11/10
B)1/55
C)1/40
D)3/55
E)1/16
Rationale: P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)
= P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)
= 1x3/16x2/15
= 1/40
Answer: C
Answer: C
Question: Mary charges $8.50 per hour to clean a house. If she works 21 hours, how much
does she earn in one week?
Options:
A)$612.50
B)$278.50
C)$178.50
D)$418.50
E)$312.50
Rationale: Multiply 21 hours x $8.50 =
Answer: $178.50
correct answer C
Answer: C
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 20%, what should be the sale price of the mixed tea?
Options:
A)23.75
B)22
C)20
D)19.2
E)None of these
Rationale: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+20)/100×16=19.2
Answer D
Answer: D
Question: Bruce purchased 8 kg of grapes at the rate of 70 per kg and 10 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1040
B)B)1050
C)C)1055
D)D)1110
E)E)1075
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 10 kg of mangoes = 55 × 10 = 550.
Total cost he has to pay = 560 + 550 = 1110
D
Answer: D
Question: A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 2 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x?
Options:
A)x/70
B)2x/63
C)3x/70
D)3x/10
E)3x/7
Rationale: cost of boat per day = x
cost per person =x/7
if three more persons afre there, cost =x/9
difference = x/7-x/9
=2x/63
Ans B
Answer: B
Question: On a test, students receive 4 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?
Options:
A)-4
B)-1
C)0
D)1
E)4
Rationale: For the minimum possible score, let us take the worst case scenario
Suppose, he gets all of the last 3 qs wrong whose correct answer options are B and one of the first 3 qs wrong whose correct option is C
In that case, he will get only 2 out of the first 3 qs right.
Therefore, minimum possible score=(4*2)-(4*1)=4
Answer E
Answer: E
Question: A train covers a distance of 12 km in 10 min. If it takes 2 sec to pass a telegraph post, then the length of the train is?
Options:
A)40
B)80
C)20
D)100
E)60
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 2 = 40 m.
Answer: Option A
Answer: A
Question: 25.25/1500 is equal to:
Options:
A)1.012526333
B)0.012625333
C)0.125263333
D)0.126253333
E)0.016833333
Rationale: 25.25/2000 = 2525/200000
= 0.016833333
ANSWER:E
Answer: E
Question: You collect pens. Suppose you start out with 5. Mike gives you another 20 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 10 pens. How many pens do you have at the end?
Options:
A)39
B)40
C)41
D)42
E)43
Rationale: Solution
Start with 5 pens.
Mike gives you 20 pens: 5 + 20 = 25 pens.
Cindy doubles the number of pens you have: 25 Ã— 2 = 50 pens.
Sharon takes 10 pens from you: 50 - 10 = 40 pens.
So you have 40 at the end.
Correct answer: B
Answer: B
Question: A truck covers a distance of 550 metres in 1 minute whereas a train covers a distance of
33 kms in 45 minutes. What is the ratio of their speed?
Options:
A)3:4
B)2:1
C)1:2
D)4:3
E)5:5
Rationale: Speed of the truck = 550 metres/min
speed of the train = 33/45 km/min = 33000/45 metres/min
speed of the truck : speed of the train
=550:33000/45 = 55:3300/45 = 5:300/45
1:60/45 = 1:4/3 = 3:4
ANSWER A
Answer: A
Question: A small person is walking on the edge of a meter-stick. He can only take centi-meter sized steps. He repeats the following process of walking forward 12 steps and backwards 6 steps. How many steps in total will he walk until he falls off the meterstick?
Options:
A)179
B)240
C)280
D)100
E)155
Rationale: His overall steps are +6
take 100 - 6
take 94/6 to lowest divisible number - 90/6
This means that it will take 15 "overall" actions to reach the 90th centimeter. -15*18 steps added later
Set steps at 90. walk 10 steps. fall off - add 10 to total
15*18 + 10 = 280 steps in total
Double checking, 6*15 = 90, meaning that it took 15 forwards and backwards to reach.
It is dangerous to oversimplify so take context. For each average steps, adding 12 each time will ensure that it is a valid process that will not resulting in falling off the meter stick. At 15 overall, he falls off. but at 14, 6*14 = 84, adding 12 we get 96 which does not result in him falling off. It is completely safe to say 15 overall steps do not result in falling off.
From there, take 10 steps an on the 11th, not counted, he falls off since he was at 90.
All that's left is to count the total steps.
each overall step has 18 steps, 12 forward and 6 backward
18*15 = 270
then add the final steps 270 +10 = 280
Answer: C
Answer: C
Question: If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)E of x, x^2, x^3, x^4 and x^5 is equal to which of the following?
Options:
A)12x
B)13x
C)14x
D)16x
E)20x
Rationale: 1 + x^4 + x^3 + x^2 + x = 81
i.e. 1 +x+ x^2+ x^3+ x^4 = 81
x+ x^2+ x^3+ x^4 = 80
x(1 +x+ x^2+ x^3) = 80
x(81-x^4) = 80
81x - x^5 = 80
x^5 = 81x -80
Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x
Average of E{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x
AnswerD
Answer: D
Question: Victor gets 90% marks in examinations. If these are 405 marks, find the maximum marks.
Options:
A)334
B)500
C)376
D)450
E)271
Rationale: Let the maximum marks be m
Then 90 % of m = 405
⇒ 90/100 × m = 405
⇒ m = (405 × 100)/90
⇒ m = 40500/90
⇒ m = 450
Therefore, maximum marks in the examinations are 450
Answer: D
Answer: D
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)33 4/3 %
B)33 1/7 %
C)33 1/3 %
D)32 1/3 %
E)33 2/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer:C
Answer: C
Question: A takes twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 6days. B can do the work alone in?
Options:
A)18
B)20
C)25
D)32
E)36
Rationale: Suppose A,B,C takes x,x/2,x/3 hours to finish the work
Then, 1/x + 2/x + 3/x = 1/6
6/x = 1/6
x = 36
Answer is E
Answer: E
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
Options:
A)Rs. 120
B)Rs. 121.3
C)Rs. 124.75
D)Rs. 125.50
E)Rs. 126.87
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: C
Question: Which of these following integers is the square of an integer?
Options:
A)20579623936
B)20325623947
C)20946623822
D)20459623463
E)20232623378
Rationale: The unit digit of any perfect square can not be 2, 3, 7, or 8.
The answer is A.
Answer: A
Question: In a certain circle there are 10 points. What is the number of the triangles connecting 2 points of the 10 points?
Options:
A)40
B)45
C)108
D)120
E)132
Rationale: IMO : B
HERE we have to select 2 points out of 10 points. Order is not important
So the answer will be 10c2 = 45
Answer B
Answer: B
Question: Can you find out how many prime numbers that are less than 75 will leave an odd reminder when divided by 5?
Options:
A)15
B)10
C)11
D)13
E)18
Rationale: C
We are looking at the numbers in the form of 5k +1 or 5k + 3
i.e The number ends in 1 or 3
If we jot down all such numbers, there are 16 in total:
1, 3, 11, 13, 21, 23, 31, 33, 41, 43, 51, 53, 61, 63, 71 and 73
Now, let us remove the ones that are not prime and we have the answer as:
3, 11, 13, 23, 31, 41, 43, 53, 61, 71 and 73
Answer: C
Question: During a special promotion, a certain filling station is offering a 8 percent discount on gas purchased after the first 10 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
Options:
A)80%
B)105%
C)115%
D)120%
E)140%
Rationale: Kim purchased 20 gallons of gas. She paid for 4 + 0.9*16 = 18.4 gallons, so the overall discount she got was 1.6/20 = 8%.
Isabella purchased 25 gallons of gas. She paid for 4 + 0.9*21 = 22.9 gallons, so the overall discount she got was 2.1/25 = 8.4%.
8.4/8*100 = 105% .
Answer: B.
Answer: B
Question: Find the next number in the series below ?
298 209 129 58 ?
Options:
A)5
B)10
C)-4
D)-10
E)0
Rationale: C
-4
298 less 209 is 89
209 less 129 is 80
129 less 58 is 71
58 less -4 is 62
The result of each subsequent equation is 9 less than the previous one.
Answer: C
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)33 1/6
B)33 1/9
C)33 1/3
D)33 1/2
E)33 1/23
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: C
Question: What should come in place of the question mark (?) in the following number series?
11 18 27 38 51 ?
Options:
A)63
B)64
C)65
D)66
E)67
Rationale: The numbers increase by 7, 9, 11, 13,...
The next number should be 51+15 = 66
The answer is D.
Answer: D