mathewhe/aqua_rat huggingface dataset:
Question: In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
(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) 7
Question: Find the surface area of a cuboid 16 m long, 8 m broad and 7 m high
(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) 832 sq.cm
Question: what is the smallest integer that is multiple of 7, 9 and 20
(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) 1260
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?
(A) 720
(B) 120
(C) 300
(D) 30
(E) 333
Rationale: 333.
Answer E
Answer: (E) 333
Question: complete the series..
2 2 12 12 30 30 ?
(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) 56
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 ?
(A) 3277
(B) 2977
(C) 12656
(D) 6077
(E) 17112
Rationale: Explanation: 40,000*(3/4)^4
Answer:C
Answer: (C) 12656
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?
(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) 1:48 p.m
Question: If log 27 = 1.431, then the value of log 9 is:
(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) 0.954
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
(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) 24 min 40 sec.
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?
(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) 25
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?
(A) 908
(B) 912
(C) 916
(D) 920
(E) 924
Rationale: 12C6=924
The answer is E.
Answer: (E) 924
Question: A man invests in a 16% stock at 128. The interest obtained by him is :
(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) 12.5%
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 = ?
(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) 1113
Question: How many multiples of 7 are there between 9 and 89, 9 and 89 inclusive ?
(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) 11
Question: 33 1/3% OF 330?
(A) 80
(B) 90
(C) 110
(D) 120
(E) 130
Rationale: 33 1/3 % = 1/3
1/3 × 330 = 110
C)
Answer: (C) 110
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 ?
(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) 498
Question: How many distinct integer values of n satisfy the inequality||n-3| + 4| ≤ 11?
(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) 8
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?
(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) 221.26
Question: The length of rectangle is thrice its breadth and its perimeter is 112 m, find the area of the rectangle?
(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) 588 sq m
Question: The length of a rectangle is halved, while its breadth is tripled. Whatis the % change in area?
(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) 50percent
Question: The diameter of a cylindrical tin is 14cm and height is 5 cm. Find the volume of the cylinder?
(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) 245
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
(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) E=9
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
(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) Rs. 15000
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.
(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) 20%
Question: What is the difference between the largest and the smallest number written with 7, 7, 0, 7?
(A) 337
(B) 628
(C) 987
(D) 693
(E) 281
Rationale: Explanation:
7770
7077
-------------
693
Answer: D
Answer: (D) 693
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?
(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) × 2!)
Question: What is 15% of 2/3 of 0.6?
(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) 0.06
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?
(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) 1/40
Question: Mary charges $8.50 per hour to clean a house. If she works 21 hours, how much
does she earn in one week?
(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) $178.50
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?
(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) 19.2
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?
(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) D)1110
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?
(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) 2x/63
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?
(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) 4
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?
(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) 40
Question: 25.25/1500 is equal to:
(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) 0.016833333
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?
(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) 40
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?
(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) 3:4
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?
(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) 280
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?
(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) 16x
Question: Victor gets 90% marks in examinations. If these are 405 marks, find the maximum marks.
(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) 450
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?
(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) 33 1/3 %
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?
(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) 36
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
(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) Rs. 124.75
Question: Which of these following integers is the square of an integer?
(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) 20579623936
Question: In a certain circle there are 10 points. What is the number of the triangles connecting 2 points of the 10 points?
(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) 45
Question: Can you find out how many prime numbers that are less than 75 will leave an odd reminder when divided by 5?
(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) 11
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?
(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) 105%
Question: Find the next number in the series below ?
298 209 129 58 ?
(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) -4
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(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) 33 1/3
Question: What should come in place of the question mark (?) in the following number series?
11 18 27 38 51 ?
(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) 66
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
(A) Rs. 500
(B) Rs. 1500
(C) Rs. 2000
(D) Rs. 2500
(E) none of the above
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
Answer = C
Answer: (C) Rs. 2000
Question: What is the smallest number Q which when increased by 5 is completely divisible by 8, 11 and 24?
(A) 264
(B) 259
(C) 269
(D) 270
(E) 282
Rationale: This question includes a number of great Number Property shortcuts that you can take advantage of:
1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.
2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.
3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.
The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.
Final Answer:
B
Answer: (B) 259
Question: In a 600 m race, the ratio of the speeds of two contestants A and B is 5 : 4. A has a start of 100 m. Then, A wins by:
(A) 200 m
(B) 20 m
(C) 403 m
(D) 20 m
(E) 23 m
Rationale: To reach the winning post A will have to cover a distance of (600 - 100)m, i.e., 500 m.
While A covers 5 m, B covers 4 m.
While A covers 500 m, B covers 4 x 500/5	m	= 400 m.
Thus, when A reaches the winning post, B covers 400 m and therefore remains 200 m behind.
A wins by 200 m.
Answer:	A
Answer: (A) 200 m
Question: The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.2200, then what is the income of P1?
(A) s.800
(B) s.2400
(C) s.4000
(D) s.5500
(E) s.4200
Rationale: Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 2200 …(i) and 4x – 2y = 2200 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 2200 -> x = 1100
P1’s income = Rs 5*1100 = Rs.5500
ANSWER:D
Answer: (D) s.5500
Question: (935421 x 625) = ?
(A) 584638125
(B) 542622125
(C) 584632125
(D) 544638125
(E) 584638125
Rationale: Explanation :
935421×625=935421×5^4=935421×(10/2)^4=(935421×10000)/16=584638125
Answer is A
Answer: (A) 584638125
Question: The number m yields a remainder p when divided by 10 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of m ?
(A) 45
(B) 57
(C) 72
(D) 85
(E) 100
Rationale: I solved this question in the following way:
Q<7 so Q can be from 0 to 6 and P<10 so P can be from 0 to 9, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 9.
m=10k + P or m= 10k + 7 to 9 and look at the answer as, place different values for k, B will give 57 which is 10*5 + 7, the other answers are out of the range
Answer: (B) 57
Question: Which of the following is a parallelogram?
(A) 120,60,120,60(angle in deg)
(B) 120,30,130,20(angle in deg)
(C) 95,95,90,90(angle in deg)
(D) a & c
(E) none
Rationale: sum of adjacent angles is 180 degrees.
ANSWER:A
Answer: (A) 120,60,120,60(angle in deg)
Question: Billy worked for three straight hours on his homework questions. If he solved 132 questions in the third hour, which was twice as many as he solved in the second hour, and three times as many questions as he solved in the first hour, how many questions did he solve total?
(A) 242
(B) 312
(C) 424
(D) 525
(E) 622
Rationale: Total questions solved= questions solved in 3rd hr+ in 2nd hr +in 1st hr
132 +132/2 +132/3= 242
A is the answer
Answer: (A) 242