mathewhe/aqua_rat huggingface dataset:
Question: A group of n students can be divided into equal groups of 3 with 1 student left over or equal groups of 6 with 1 students left over. What is the sum of the two smallest possible values of n?
(A) 33
(B) 46
(C) 49
(D) 53
(E) 86
Rationale: 3x+1 = 6y+1...........ie: 3x-6y = 0
x,y must be >1 and y is even ie ( 2,4,6,..etc)
if y = 2 thus x = 4 and thus n = 13
if y = 4 thus x is =8 and thus n= 25
13+25 = 38
E
Answer: (E) 86
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 15% food additives; 19% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
(A) 8°
(B) 10°
(C) 18°
(D) 36°
(E) 72°
Rationale: 14% microphotonics;
24% home electronics;
15% food additives;
19% genetically modified microorganisms;
8% industrial lubricants;
100-(14+24+15+19+8)=20% basic astrophysics.
10% of 360° is 72°.
Answer: E.
Answer: (E) 72°
Question: How much water must be added to 64 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
(A) 16 litres
(B) 12 litres
(C) 15 litres
(D) 18 litres
(E) None of these
Rationale: C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 64 litres of milk
= (1⁄4 × 64) litres = 16 litres.
Answer A
Answer: (A) 16 litres
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 22
(B) 71
(C) 54
(D) 77
(E) 99
Rationale: S = 240/16 * 18/5 = 54 kmph
Answer: C
Answer: (C) 54
Question: If 2x + y = 7 and x + 2y = 5, then 5xy/3 =?
(A) A) 5
(B) B) 2
(C) C) 17/5
(D) D) 18/5
(E) E) 4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
(5*3*1)/3
= 15/3
=5
A
Answer: (A) A) 5
Question: The difference between a number and its two-fifth is 510. What is 50% of that number?
(A) 426
(B) 425
(C) 427
(D) 428
(E) 429
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
50% of 850 = 425.
Answer:B
Answer: (B) 425
Question: A soccer coach is preparing his starting lineup of 11 players chosen from 15 players. He considers 8 of his players good at defense and 7 of his players good at offense. If he wants to pick 6 players best at defense and 5 players best at offense, how many different ways can he do this?
(A) 264
(B) 328
(C) 460
(D) 588
(E) 642
Rationale: (8c6)*(7c5)
[8!/(6!*2!)]*[7!/(5!*2!)]
28*21
588
D
Answer: (D) 588
Question: A certain company has budgeted $1380 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $250, how much was the company under budget or over budget?
(A) $95 under budget
(B) $35 under budget
(C) $35 over budget
(D) $95 over budget
(E) $125 over budget
Rationale: The budget for 3 months is (3/12)*$1380 = $345
The company is $95 under budget.
The answer is A.
Answer: (A) $95 under budget
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
(A) 2
(B) 4
(C) 5
(D) 8
(E) 10
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: (D) 8
Question: The average mark of a class of twenty two students is 65. If four students whose marks are 25, 32,28 and 34 are removed , then find the approximate average mark of the remaining students of the class.
(A) 71
(B) 73
(C) 57
(D) 70
(E) 80
Rationale: Exp. Total mark of 22 students = 65*22 = 1430,
Total mark after the removal of 4 students = 1430 –(25+32+28+34 )
= 1430 – 119 = 1311
Approximate average mark = 1311/(22-4) = 1311/ 18 = 73
Answer: B
Answer: (B) 73
Question: A factory produces 6000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
(A) 4436 toys
(B) 1500 toys
(C) 6113 toys
(D) 2354 toys
(E) 1375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
6000 /4 = 1500 toys
correct answer B
Answer: (B) 1500 toys
Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: B->1
G->5
P->x; 5<x<11
R->11
NOW, 88000=11*8^2*5^4*1^n
hence
no of balls drawn,
B= CANT BE DETERMINED
G= 4
P= 2 (Only possible value is 8 )
R= 1
hence B
Answer: (B) 2
Question: Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 80 of the members do not use either, then the number of members using both the weight room and the pool must be between:
(A) 40 to 100
(B) 240 to 280
(C) 230 to 260
(D) 240 to 260
(E) 200 to 260
Rationale: W=260
P=300
ALL=400
N(NEITHER)=AT LEAST 80
BOTH=?
W+P-BOTH+N=ALL
260+300-BOTH+80=400
BOTH=240
now pay attention to the fact, that both at most can be 260, since W=260
D
Answer: (D) 240 to 260
Question: From a bunch of six keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys?
(A) 1/20
(B) 1/30
(C) 1/60
(D) 1/80
(E) 1/120
Rationale: The probability is 1/6*1/5*1/4 = 1/120.
The answer is E.
Answer: (E) 1/120
Question: What is the smallest integer k for which 64^k > 4^19?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 64^k > 4^19
4^(3k) > 4^19
3k > 19
k = 7
The answer is D.
Answer: (D) 7
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 20 cm
(B) 15 cm
(C) 30 cm
(D) 40 cm
(E) 45 cm
Rationale: 1: 2/5 = 5: 2
2/7 * 70 = 20
ANSWER A
Answer: (A) 20 cm
Question: There are 18 balls in a jar. You take out 3 black balls without putting them back inside, and now the probability of pulling out a black ball is 1/3. How many blue balls were there in the beginning?
(A) 12.
(B) 9.
(C) 8.
(D) 7.
(E) 6.
Rationale: 8 = 3 blue balls + 15 / 3
Answer: C
Answer: (C) 8.
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 18:15
(C) 14:11
(D) 18:67
(E) 18:12
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11.Answer: A
Answer: (A) 18:11
Question: If each term in the sum Q=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Min value of 'n' can be 10 i.e 4*22+6*12 =Q=> 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
Hence C.
Answer: (C) 40
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 33
(B) 88
(C) 27
(D) 10
(E) 88
Rationale: 4/12 + x/15 = 1
x = 10
Answer:D
Answer: (D) 10
Question: There are 89 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
(A) 2
(B) 4
(C) 8
(D) 59
(E) 32
Rationale: lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 89
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x
Exactly Cat and Snake = y
all three= 3
so 89=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 59
answer:D
Answer: (D) 59
Question: The area of sector of a circle whose radius is 15 metro and whose angle at the center is 42Â° is?
(A) 52.6
(B) 52.9
(C) 52.8
(D) 52.1
(E) 82.5
Rationale: 42/360 * 22/7 * 15 * 15 = 82.5 m2
Answer: E
Answer: (E) 82.5
Question: The expression 10^14−100 is divisible by all of the following integers EXCEPT
(A) 2
(B) 3
(C) 4
(D) 8
(E) 7
Rationale: Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (E) is correct.
Answer: (E) 7
Question: David is able to sell a hand-carved statue for $1150 which was a 15% profit over his cost. How much did the statue originally cost him?
(A) $496.30
(B) $512.40
(C) $1000
(D) $574.90
(E) $588.20
Rationale: Cost price = 1150/115*100 = 1000
Answer : C
Answer: (C) $1000
Question: A certain school implemented a reading program for its students, with the goal of getting each student to read 7 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?
(A) 20cs
(B) cs/2
(C) 84cs
(D) (2cs)/12
(E) (24c)/s
Rationale: Ans: C
Solution: simple multiplication s students , c classes , 7 books/ month= 84 books a year
total number of books = 84cs
Answer: (C) 84cs
Question: A sum of money place at compound interest doubles itself in 6 years. In how many years will it amount to eight times itself?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 30
Rationale: 100 ---- 200 ---- 6
400 ---- 6
800 ---- 6
------
18 years
Answer: C
Answer: (C) 18
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 5
(B) 2
(C) 9
(D) 7
(E) 1
Rationale: 1250 = D(100/4)2
D = 2
Answer: B
Answer: (B) 2
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
(A) 8118
(B) 8127
(C) 8618
(D) 8112
(E) 8128
Rationale: A = 7500(26/25)2
= 8112
Answer: D
Answer: (D) 8112
Question: There are 6 red shoes & 4 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
(A) 1/3
(B) 1/4
(C) 1/2
(D) 1/5
(E) 1/6
Rationale: taking 2 red shoe the probablity is 6C2
from 10 shoes probablity of taking 2 red shoe is 6C2/10C2=1/3
ANSWER:A
Answer: (A) 1/3
Question: If 5^y+ 6^(y) = 61, which of the following is the value of y?
(A) 5
(B) 1
(C) 3
(D) 4
(E) 2
Rationale: Plugging in the various option into the equation to find out which is correct:
5^y+ 6^(y) = 61
5^2+ 6^(2) = 61 Ans. E
Answer: (E) 2
Question: 7 teams compete in a track competition. If there are 17 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 3(max wins) x 5 = 15 (5 teams win three events)
One team wins the other two events.
The answer is D.
Answer: (D) 6
Question: In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 5 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?
(A) 3
(B) 5
(C) 10
(D) 13
(E) 15
Rationale: The average number of books per student was 2means that total of 2*20=40 books were borrowed;
2+8+5=15 students borrowed total of 2*0+8*1+5*2=18 books;
So 40-18=22 books are left to distribute among 20-15=5 students, these 5 arethe rest who borrowed at least 3 books;
Tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed. Minimum these 4 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 4*3=12 books. So the 5th student could have borrowed is 22-12=10 books.
Answer: C.
Answer: (C) 10
Question: A certain basketball team that has played 2/3 of its games has a record of 18 wins and 2 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
(A)  7
(B)  6
(C)  5
(D)  4
(E)  3
Rationale: 18 wins, 2 losses - total 20 games played.
The team has played 2/3rd of all games so total number of games = 30
3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 2 games so it can lose another 5 at most.
Answer (C)
Answer: (C)  5
Question: A ferry can transport 100 tons of vehicles. Automobiles range in weight from 1,600 to 3,000 pounds. What is the greatest number of automobiles that can be loaded onto the ferry?
(A) 110
(B) 128
(C) 115
(D) 130
(E) 120
Rationale: to get maximum vehicles we must take into consideration the minimum weight i.e 1600 pounds here
since , 1 ton = 2000 pounds
100 tons will be 200,000 pounds
from the answer choices:
let max number of vehicles be 120
total weight will be = 120*1600 = 192000 pounds , which is lesser than the maximum weight allowed .
Ans: E
Answer: (E) 120
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many L cubes are painted on only 2 faces?
(A) 12
(B) 8
(C) 6
(D) 10
(E) 16
Rationale: 1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....
The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube.L= 4 + 4 + 4 = 12. Answer A
Answer: (A) 12
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 8 on Wednesday, what would be the value of D calculated on the following Saturday?
(A) 1680
(B) 1830
(C) 2250
(D) 2400
(E) 3260
Rationale: On Saturday, the value would be 7*6*5*8 = 1680
The answer is A.
Answer: (A) 1680
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 100kmph, find the rate at which the train B runs.
(A) 40
(B) 60
(C) 120
(D) 80
(E) 150
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 80 kmph, speed of B must be 100*(3/2) = 1520 kmph
E
Answer: (E) 150
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 30, 55, 60, then the average marks of all the students is:
(A) 53.33
(B) 54.68
(C) 55
(D) 47.81
(E) None of these
Rationale: Explanation:
Required average = (55 × 30 + 60 × 55 + 45 × 60/55 + 60 + 45)
= (1650 + 3300 + 2700/160)
= 7650/160
= 47.81
Answer: D
Answer: (D) 47.81
Question: Machine A takes 100 hours to complete a certain job and starts that job at 7AM. After two hour of working alone, machine A is joined by machine B and together they complete the job at 6PM. How long would it have taken machine B to complete the jobif it had worked alone for the entire job?
(A) 10.11
(B) 9.99
(C) 11.1
(D) 44.11
(E) 1.01
Rationale: Let us assume total job = 100 units
A finishes 100 units in 100 hrs(given)
Hence A (working rate)= 1 units /hr
Now Given that A works for 2 hr( so 2 units done) then A and B finish total work in 15 hours. Hence A and B finish 98 units in 9 hours. Of these 1x9=9 units were done by A. Hence B did 89units in 9 hours.
Hence B(working rate)= 89/9 units /hr
Hence B takes 100x9/89 = 10.11 hours to complete the job.
Answer A.
Answer: (A) 10.11
Question: An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?
(A) Rs.3776
(B) Rs.3729
(C) Rs.3720
(D) Rs.3778
(E) Rs.3992
Rationale: A = P(1 + TR/100)
=> 3600 = 3000[1 + (4 * R)/100] => R = 5%
Now R = 6%
=> A = 3000[1 + (4 * 6)/100]
= Rs.3720.
Answer: C
Answer: (C) Rs.3720
Question: Find the area of circle whose radius is 7m?
(A) 187
(B) 154
(C) 177
(D) 288
(E) 298
Rationale: 22/7 * 7 * 7
= 154
Answer:B
Answer: (B) 154
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 5 consecutive spaces in a random direction, what is the probability the piece ends no more than 5 spaces from the square numbered 49?
(A) 15%
(B) 8%
(C) 11%
(D) 12%
(E) 13%
Rationale: No more than 5 spaces from 49 means in the rangefrom 49-5=44 to 49+5=54, inclusive. Total numbers in this range 54-44+1=11, the probability favorable/total=11/100
Answer: C
Answer: (C) 11%
Question: There are 8 women and 7 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 332
(B) 450
(C) 362
(D) 476
(E) 588
Rationale: 8C2 * 7C2 = 28*21 = 588
The answer is E.
Answer: (E) 588
Question: The average marks of 30 students are 45 but after checking there are two mistakes found. After adjustment if a student got 45 more markes and other student got 15 less marks, then What will be the adjusted average?
(A) 45
(B) 44
(C) 47
(D) 46
(E) None of these
Rationale: Answer
Total number of all students of the class = 30 x 45 = 1350
∴ New average after adjustment = (1350 - 45 + 15)/30 = 1320/30 = 44
Correct Option: B
Answer: (B) 44
Question: Suppose there are 4 books on fairy tales, 5 novels and 3 plays. They have to be arranged so that the books on fairy tales are together, novels are together and plays are together, but we no longer require that they should be in a specific order. In how many ways can this be done?
(A) 103680
(B) 113689
(C) 125569
(D) 136690
(E) None
Rationale: Explanation :
First, we consider the books on fairy tales, novels and plays as single objects.
These three objects can be arranged in 3!=6 ways.
Let us fix one of these 6 arrangements.
This may give us a specific order, say, novels -> fairy tales -> plays.
Given this order, the books on the same subject can be arranged as follows.
The 4 books on fairy tales can be arranged among themselves in 4!=24 ways.
The 5 novels can be arranged in 5!=120 ways.
The 3 plays can be arranged in 3!=6 ways.
For a given order, the books can be arranged in 24*120*6=17280 ways.
Therefore, for all the 6 possible orders the books can be arranged in 6*17280= 103680 ways.
Answer : A
Answer: (A) 103680
Question: If five machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job?
(A) 45
(B) 60
(C) 75
(D) 80
(E) 100
Rationale: using the std formula
m1d1h1/w1=m2d2h2/w2
substituting the values we have
5*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)
10/3=10/3*x
x=1 hour
so 60 minutes
ANSWER:B
Answer: (B) 60
Question: In two alloys, copper and tin are related in the ratios of 4:1 and 1:3. 10kg of Ist alloy, 16 kg of 2nd alloy and some pure copper melted together. An alloy obtained in which the ratio of copper and tin was 3:2. Find the weight of the new alloy.
(A) 34kg
(B) 35kg
(C) 36kg
(D) 30kg
(E) 32kg
Rationale: suppose x kg of pure copper is melted with 10kg of Ist alloy and 16 kg of 2nd alloy , then
Pure cooper in new alloy = 10*4/5 + 16*1/4 +x = 12+x kg
Pure tin in new alloy = 10*1/5+ 16*3/4 = 14 kg
As per given condition
(12+x)/14 = 3/2
24+2x= 42
x=9 kg
Total weight of new alloy = 10+16+9=35 kg
ANSWER:B
Answer: (B) 35kg
Question: The least common multiple of positive integer f and 3-digit integer n is 690. If n is not divisible by 3 and f is not divisible by 2, what is the value of n?
(A) 115
(B) 230
(C) 460
(D) 575
(E) 690
Rationale: The LCM of n and f is 690 = 2*3*5*23.
f is not divisible by 2, thus 2 goes to n
n is not divisible by 3, thus 3 goes to f.
From above:
n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.
Answer: B.
Answer: (B) 230
Question: x/2y = 2a,then 2x/x-2ay=?
(A) 4
(B) 8
(C) 16
(D) 2
(E) 6
Rationale: x/2y=2a,
Then x = 4ay,
Now, 2x/x-2ay = (2*4ay)/(4ay-2ay) = 8ay/2ay = 4
ANSWER:A
Answer: (A) 4
Question: Which no. need to add to 859622 to get a no. exactly divisible by 456?
(A) 546577
(B) 674645
(C) 566578
(D) 465766
(E) 859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: (E) 859622
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 231525, then population in 1978 was?
(A) 120000
(B) 228788
(C) 266891
(D) 267689
(E) 200000
Rationale: X * (105/100) * (105/100) * (105/100) = 232525
X = 231525/1.157625
X = 200000
Answer:E
Answer: (E) 200000
Question: In how many different ways can 5 identical blue pants and 5 identical red pants be shared among 10 children such that each child receives a pant?
(A) 628800
(B) 4628800
(C) 2628800
(D) 3628800
(E) 1628800
Rationale: GGG RRR
Therefore total number of ways is
6! but there are two groups of 3 identical things.
Therefore total number of "different" ways is
10!/ (5!) (5!) = 3628800 ANS:D
Answer: (D) 3628800
Question: During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 20 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
(A) 8.5%
(B) 50%
(C) x/12%
(D) 60/x%
(E) 400/x%
Rationale: Say x = 5 miles (so no remainder of the trip).
Time to cover x = 5 miles at 20 miles per hour = (time) = (distance)/(rate) = 5/20 = 1/4 hours = 10 minutes.
Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/60 = 1/12 hours = 5 minutes.
(Or simply, half rate will result in doubling the time.)
So, we can see that the time to cover x = 5 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 5 miles at 60 miles per hour (5 minutes).
Now, plug x = 4 miles into the answer choices to see which one yields 100%. Only answer E works.
Answer: E.
Answer: (E) 400/x%