mathewhe/aqua_rat huggingface dataset:
Question: If a copier makes 3 copies every 4 seconds, then continues at this rate, how many minutes will it take to make 9,000 copies?
(A) 60
(B) 100
(C) 120
(D) 200
(E) 3,000
Rationale: Let x = seconds to make 9000 copies.
We get: 3/4 = 9000/x
Cross multiply to get: 3x = (4)(9000)
Simplify: 3x = 36,000
Solve: x = 12,000 SECONDS
There are 60 seconds in a minute.
12,000/60 = 200
So, it takes 200 MINUTES to make 9000 copies
Answer: D
Answer: (D) 200
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 92.5 kmph
(B) 17.5 kmph
(C) 15.5 kmph
(D) 12.5 kmph
(E) 22.5 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D
Answer: (D) 12.5 kmph
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
(A) 1/3
(B) 1/5
(C) 4/7
(D) 7/4
(E) 2/7
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
C
Answer: (C) 4/7
Question: How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?
(A) 72
(B) 64
(C) 36
(D) 18
(E) 6
Rationale: Since A and E must be among 3 letters then the third letter must be out of B, C and D. 3C1 = 3 ways to choose which one it'll be. Now, 3 different letters (A, E and the third one) can be arranged in 3!=6 ways, so the final answer is 3*6=18.
Answer: D.
Answer: (D) 18
Question: Indu gave Bindu Rs.4375 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) 1
(B) 2
(C) 7
(D) 4
(E) 9
Rationale: 4375 = D(100/4)2
D = 7
Answer:C
Answer: (C) 7
Question: A meeting has to be conducted with 4 managers. Find the number of ways in which the managers may be selected from among 7 managers, if there are 2 managers who refuse to attend the meeting together.
(A) 18
(B) 21
(C) 25
(D) 30
(E) 35
Rationale: The total number of ways to choose 4 managers is 7C4 = 35
We need to subtract the number of groups which include the two managers, which is 5C2 = 10.
35 - 10 = 25
The answer is C.
Answer: (C) 25
Question: In how many different ways can the letters of the word ORGANISE be arranged in such a way that all the vowels always come together and all the consonants always come together?
(A) 576
(B) 1152
(C) 2880
(D) 1440
(E) None of these
Rationale: The word ORGANISE has 4 vowels and 4 consonants.
Now, both groups (vowels and consonants) can be treated as two letters. This can be arranged in 2! ways.
Now, the 4 letters of each group can be arranged.in 4! ways.
So, total possible ways of arrangement
= 2! × 4! × 4!
= 2 × 24 × 24 = 1152.
Answer B
Answer: (B) 1152
Question: In a certain school, 20% of the students are below 8 yrs of age. The number of students above 8 yrs of age is (2/3) of the number of students of 8 years age which is 96. What is the total number of students in the school?
(A) 237
(B) 200
(C) 267
(D) 176
(E) 161
Rationale: Explanation:
Let total students be x.
⇒ 0.2x + 2323 × 96 + 96 = x
⇒ x = 200
Answer: B
Answer: (B) 200
Question: The combined salaries of three brothers is $180,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?
(A)  20,000
(B)  22,000
(C)  25,000
(D)  30,000
(E)  40,000
Rationale: Mr. Small = x;
Mr. Middle = 3/2*x;
Mr. Big = 2x.
x + 3/2*x + 2x = 180 --> x=40
Answer: E
Answer: (E)  40,000
Question: Which of the following is closer to (22!+21!)/(22!-21!)?
(A) 49
(B) 36
(C) 1
(D) 16
(E) 25
Rationale: Notice that 22! = (22)(21!), so we can factor out 21! from top and bottom.
(22!+21!)/(22!-21!)=[21!(22+1)]/[21!(22-1)]
= (22+1)/(21-1)
= 23/21
≈ 1
Answer: C
Answer: (C) 1
Question: If 3 strawberry vines produce 30 fruit and 20 strawberry vines produce 200 fruit, how many fruit do 50 strawberry vines produce?
(A) 5
(B) 50
(C) 500
(D) 5000
(E) 3
Rationale: 3 x ? = 30
20 x ? = 200
50 x ? = ?
3 x 10 = 30
20 x 10 = 200
Therefore, each strawberry vine makes 10 fruits.
50 x 10 = 500
answer: c
Answer: (C) 500
Question: A credit card number has 6 digits (between 1 to 9 inclusive). The first two digits are 12 in that order, the third digit is bigger than 6, the fourth digit is divisible by 3, and the fifth digit is 4 times the sixth. How many different credit card numbers are possible?
(A) 12
(B) 15
(C) 18
(D) 24
(E) 36
Rationale: The first two digits are fixed.
The third digit can be 7, 8, or 9 so there are 3 choices.
The fourth digit can be 3, 6, or 9 so there are 3 choices.
The fifth digit depends entirely on the sixth digit.
The sixth digit can be 1 or 2 so there are 2 choices.
The number of possibilities is 3*3*2 = 18
The answer is C.
Answer: (C) 18
Question: The breath of a rectangle is three- seventh of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the length is 10 units?
(A) 310 sq.units
(B) 110 sq.units
(C) 210 sq.units
(D) 105 sq.units
(E) 205 sq.units
Rationale: Given that the area of the square = 4900 sq.units
=> Side of square = √4900 = 70units
The radius of the circle = side of the square = 49 units breath of the rectangle = 3/7 * 49 = 21units
Given that length = 10 units
Area of the rectangle = lb = 21 * 10 = 210 sq.units
Answer:C
Answer: (C) 210 sq.units
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 12?
(A) 8
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: i'm not sure i got the question right, if it is what i think it is, then 8 should be the right answer
0,1,2,3,4,5, will not have 2 slip sum of 10, add another (either 6,7,8 or 9) and we'll have a pair with sum 12
Ans:8
Answer: (A) 8
Question: Out of the fractions 4/7, 5/13, 6/11, 3/5 and 2/3 which is the second smallest fraction ?
(A) 4/7
(B) 5/13
(C) 6/11
(D) 3/5
(E) None
Rationale: Answer
4/7 = 0.57,
5/13 = 0.38,
6/11 = 0.54,
3/5 = 0.6 and
2/3 = 0.67
Clearly, the second smallest fraction is 6/11
Correct Option: C
Answer: (C) 6/11
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
(A) 2978
(B) 2681
(C) 2689
(D) 1000
(E) 2760
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100
= 140
X = 1000
Answer: D
Answer: (D) 1000
Question: The difference between a number and its two-fifth is 510. What is 10% of that number?
(A) 12.75
(B) 85
(C) 204
(D) 224
(E) 95
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
10% of 850 = 85.
ANSWER:B
Answer: (B) 85
Question: A train of 40 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
(A) 6
(B) 3
(C) 4
(D) 3.9
(E) 3.6
Rationale: D = 40 * 60 + 1500 = 3900 m
T = 3900/60 * 18/5 = 234 sec = 3.9 mins
Answer:D
Answer: (D) 3.9
Question: Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?
(A) 144
(B) 122.5
(C) 105.1
(D) 72
(E) 134
Rationale: Mixture A: 2:5 ratio of Milk:Water
Mixture B: 5:4 ratio of Milk:water
90 gallons mixture B with a ratio of 5:4 = 50 gallons of milk and 40 gallons of water 90/(5+4) = 10. 10*5 = 50 and 10*4 = 40.
(50+(2/7x))/(90+x) = .40
50+(2/7x)=.4(90+x)
50+(2/7x)=(2/5x)+36
50+(10/35x)=(14/35x) +36
4/35x=14
4x=14*35
4x=490
x=122.5 gallons
ANSWER:B
Answer: (B) 122.5
Question: 0.1 decates ago, Vijaya was quadrice as old as her daughter Simran. 0.6 decades hence, Vijaya’s age will beat her daughter’s age by 0.9 decades. The proportion of the current ages of Vijaya and Simran is : [ 0.1 Decates =1 Year; quadrice = 4 times]
(A) 8:1
(B) 10:2
(C) 11:4
(D) 13:4
(E) None of these
Rationale: Explanation:
Let, Ages of Vijaya and Simran – 1 year ago was 4A and A years correspondingly.
Then, [(4A + 1) + 6] – [(A + 1) + 6] = 9
3A = 9 A = 3
Needed Ratio = (4A + 1) : (A + 1) = 13 : 4.. Answer: D
Answer: (D) 13:4
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
(A) 5.456%
(B) 6.124%
(C) 6.125%
(D) 7.256%
(E) 8.234%
Rationale: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Answer: (C) 6.125%
Question: 46 x 46 = ?
(A) 2500
(B) 2516
(C) 1600
(D) 36
(E) 2116
Rationale: 46 x 46	= (46)2
= (50 - 4)2
= (50)2 + (4)2 - (2 x 50 x 4)
= 2500 + 16- 400
= 2516 - 400
= 2116
E)
Answer: (E) 2116
Question: Points M(9,4) and N(5,8) lie on the xy - plane. What is the midpoint of line segment MN?
(A) (7,6)
(B) (0,5)
(C) (0, (136^(1/2))/2)
(D) (3/2,0)
(E) (1,5)
Rationale: The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states:
• The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints.
• Likewise, the y-coordinate is the average of the y-coordinates of the endpoints.
So, x=(9+5)/2=7 and y=(4+8)/2=6 --> coordinates of the midpoint are (7, 6).
Answer: A.
Answer: (A) (7,6)
Question: A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(A) 2:6
(B) 2:6
(C) 2:3
(D) 2:4
(E) 2:9
Rationale: Let the principal be P and rate of interest be R%.
Required ratio = [(P * R * 6)/100] / [(P * R * 9)/100]
= 6PR/9PR = 6/9
= 2:3
Answer: C
Answer: (C) 2:3
Question: The ratio between a two-digit number and the sum of the digits of that
number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number?
(A) 47
(B) 36
(C) 58
(D) 25
(E) 14
Rationale: Let the ten's digit be x. Then, unit's digit = (x + 3).
Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3.
11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3.
Hence, required number = 11x + 3 = 36.
Answer is B.
Answer: (B) 36
Question: The ratio of number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents left, the ratio became 1 : 3. How many people were originally present at the party?
(A) 6
(B) 9
(C) 12
(D) 10
(E) 11
Rationale: Let number of ladies = x
then, number of gents = 2x
Now, x−2/2x−2=1/3⇒ 3x - 6 = 2x - 2
⇒ x = 4
∴ Total number of people originally present = 4 + 8 = 12
Answer C
Answer: (C) 12
Question: 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 16
(B) 30
(C) 86
(D) 27
(E) 82
Rationale: 3W = 2M
15M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
15 * 21 * 8 = 14 * x * 6
x = 30
Answer: C
Answer: (C) 86
Question: A student traveled 30 percent of the distance of the trip alone, continued another 20 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip?
(A) 240
(B) 200
(C) 160
(D) 100
(E) 50
Rationale: Let x be the total length of the trip.
0.3x + 20 miles + 0.5x = x
20 miles = 0.2x
x = 100 miles
The answer is D.
Answer: (D) 100
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 27,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
(A) Rs. 2000
(B) Rs. 4000
(C) Rs. 6000
(D) Rs. 3000
(E) None of these
Rationale: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 27,000 = Rs. 9,000
Salary of A = Rs. (15000 – 9000) = Rs. 6000
ANSWER: C
Answer: (C) Rs. 6000
Question: On dividing $200 between A and B such that twice of A's share is less than 2 times the total share of A and B by 100. Find B's share.
(A) 100
(B) 120
(C) 70
(D) 90
(E) 50
Rationale: Let A's share be X and B's share be Y.
=>2*X=2*(X+Y)-100
=>2Y=100
=>Y=50
Option E
Answer: (E) 50
Question: If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 217, what is the common ratio of the G.P?
(A) 3
(B) 1/3
(C) 2
(D) 6
(E) 1/6
Rationale: 217=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)
Factorize the same terms
217=1+(a4+a5+a6)/(a1+a2+a3)
Write every term with respect to r
a1=a1
a2=a1*r^1
a3=a1*r^2
.........
217=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))
216=(r^3 (1+r^1+r^2))/((1+r^1+r^2))
216=r^3
r=6
D
Answer: (D) 6
Question: Find the sum of all 3 digit natural numbers, which are divisible by 8
(A) 61376
(B) 54411
(C) 612314
(D) 64170
(E) 64171
Rationale: The three digit natural numbers divisible by 8 are
104, 112, 120, …. 992.
Let Sndenote their sum. That is, Sn = 104 112 120 128 , 992 g + + + + + .
Now, the sequence 104, 112, 120, g, 992 forms an A.P.
a=104, d=8, l=992
n=l-a/d
n=112
S112=n/2(a+l)=61376
ANSWER A 61376
Answer: (A) 61376
Question: If x=3y=4z, what is z+y, in terms of x?
(A) 3x/5
(B) 4x/9
(C) 11x/13
(D) 7x/12
(E) 5x/11
Rationale: x=3y=4z
x/4 = z
and y = x/3
z+y = x/4 + x/3 = 7x/12
Answer is D
Answer: (D) 7x/12
Question: What amount does Kiran get if he invests Rs.6450 at 15% p.a. compound interest for two years, compounding done annually?
(A) 8400
(B) 8900
(C) 4560
(D) 8530
(E) 9890
Rationale: A= P{1 + R/100}n
=> 6450{1 + 15/100}2
= Rs.8530
Answer: D
Answer: (D) 8530
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 18 more transactions than Cal. How much transactions did Jade handled?
(A) 80
(B) 81
(C) 82
(D) 83
(E) 84
Rationale: Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 18 more transactions than Cal.
Jade = 66 + 18
= 84
Jade handled = 84 transactions.
Answer: E
Answer: (E) 84
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 125
(B) 879
(C) 476
(D) 255
(E) 789
Rationale: Explanation:
3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476
Answer : C
Answer: (C) 476
Question: Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1245
(B) 1345
(C) 1455
(D) 1577
(E) 1647
Rationale: Let the smaller number be x. Then larger number = (x + 1375).
x + 1375 = 6x + 15
5x = 1360
x = 272
Large number = 272+1375 = 1647
E
Answer: (E) 1647
Question: The average weight of 10 persons increases by 3.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 76 kg
(B) 80 kg
(C) 85 kg
(D) 97 kg
(E) None
Rationale: Solution
Total weight increased	= (10 x 3.2)kg
= 32 kg.
Weight of new person	= (65 + 32)kg
= 97 kg.
Answer D
Answer: (D) 97 kg
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
(A) 40
(B) 42
(C) 44
(D) 48
(E) 52
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: (B) 42
Question: A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper?
(A) 140 cm2
(B) 240 cm2
(C) 560 cm2
(D) 160 cm2
(E) None of these
Rationale: When folded along breadth, we have :
2(l⁄2 + b) = 34 or l + 2b = 34 ....(i)
When folded along length, we have :
2(l + b⁄2) = 38 or 2l + b = 38 ....(ii)
Solving (i) and (ii), we get :
l = 14 and b = 10.
∴ Area of the paper = (14 × 10) cm2 = 140 cm2
Answer A
Answer: (A) 140 cm2
Question: If tomorrow will be a Sunday, what day was the day before yesterday?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday
Rationale: Explanation:
Tomorrow will be a Sunday
=>Today is a Saturday
=> Yesterday was a Friday
=> The day before yesterday was Thursday
Answer: Option D
Answer: (D) Thursday
Question: There are b cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
(A) n(n-1)
(B) n(n+1)
(C) n(n-1)/2
(D) n(n+1)/2
(E) b(b-1)
Rationale: First of all, the possible number of airlines is b. Then, the possible number of airlines departing from one city to another becomes (b-1). Hence, the answer is b(b-1), which makes E
Answer: (E) b(b-1)
Question: What approximate value should come in place of the question mark (?) in each of the following equations ?
52.861 + 0.2563 + 8.1 + 57.35 + 0.0087 = ?
(A) 119
(B) 116
(C) 121
(D) 115
(E) 120
Rationale: Explanation :
52.8 + 3 + 8 + 57.4 + 0087 = 118.5 + 0.0087 = 119
Answer : Option A
Answer: (A) 119
Question: If 1/4 of the passengers on a ship are from North America, 1/8 are Europeans, 1/12 are from Africa, 1/6 are from Asia and the remaining 36 people are citizens of other continents, then how many passengers are on board the ship?
(A) 92
(B) 96
(C) 100
(D) 104
(E) 108
Rationale: 1/4 + 1/8 + 1/12 + 1/6 = (6+3+2+4)/24 = 15/24
Let x be the number of passengers on the ship.
36 = (9/24)x = 3x/8
x = 96
The answer is B.
Answer: (B) 96
Question: Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of z crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of z?
(A) z/2
(B) z
(C) 3z/2
(D) 2z
(E) 3z
Rationale: Lets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Amy carries 3 crumbs per trip. Also let Arthur make 2 trips and so Amy makes 4 trips.
Thus total crumbs carried by Arthur (z) = 2 x 2 = 4, total crumbs carried by Amy = 3 x 4 = 12. 12 is 3 times 4, so E
Answer: (E) 3z
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 8 days
(B) 5 days
(C) 2 days
(D) 9 days
(E) 1 days
Rationale: 3/12 + (3 + x)/16 = 1
x = 9 days
Answer: D
Answer: (D) 9 days
Question: A book is bought for $60 and sold for $63. What is the profit in percentage?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: 63/60 = 1.05
The answer is B.
Answer: (B) 5
Question: In how many ways a hockey team of eleven can be elected from 16 players?
(A) 4368
(B) 4267
(C) 5368
(D) 4166
(E) None of these
Rationale: Solution
The required number of selections
= 3C1 × 4C1 × 2C1 (6C3 + 6C2 + 6C0) = 42 × 4!. Answer A
Answer: (A) 4368
Question: Iron company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
(A)  16
(B)  64
(C)  256
(D)  576
(E)  4096
Rationale: MAGOOSHOFFICIAL SOLUTION:
Iron company has four empty trucks that will head out in the morning, all four to the same destination.Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.
N = 4*4*4*4 = 16*16 = 256
Answer = (C)
Answer: (C)  256
Question: In an increasing sequence of 8 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 4 integers in the sequence?
(A) 585
(B) 580
(C) 586
(D) 587
(E) 589
Rationale: Solution:
In solving this problem we must first remember that when we have 8 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
Integer 4: x + 3
Integer 5: x + 4
Integer 6: x + 5
Integer 7: x + 6
Integer 8: x + 7
We are given that the sum of the first 4 integers is 570. This means that:
x + x+1 + x+2 + x+3 = 570
4x + 6 = 570
4x = 564
x = 141
The sum of the last 4 integers can be expressed and simplified as:
x+4 + x+5 + x+6+ x+7 = 4x + 22
Substituting 141 for x yields:
(4)(141) + 22 = 586
Answer: C
Answer: (C) 586
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 7?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 6
Highest two digit number divisible by 7 is 63, so we count down the correct answers from there and see if they are feasible.
63 -yes
56 -yes
49 -no
42 - yes
35 - yes
28 - no
21 - yes
14- yes
Correct answer is C.
Answer: (C) 6
Question: Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 3 days?
(A)  6
(B)  9
(C)  10
(D)  12
(E)  15
Rationale: This is an inverse proportional problem......
5 pipes in 12 days; So for 3 days, it will be = 12 x 5 / 3 = 20
So, 20-5 = 15
Answer E
Answer: (E)  15
Question: Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?
(A) Between 0 and 90
(B) Between 0 and 30
(C) Between 0 and 60
(D) Between 0 and 75
(E) Between 0 and 45
Rationale: Explanation :
It says P&Q falls outside the intersection area of the circle.
The maximum point where P&Q can be in the circle is represented by the 2 small dashes P1 and Q1, when they can be on the circumference of the other circle.
Suppose P & Q are on the circumference of the other circle. (Represented by P1 and Q1)
Then AP1 = r1 (Radius of 1st circle)
AQ1 = r2 (Radius of 2nd circle)
Also P1Q1 = r1 = r2 (As radius of both the circles are same)
So AP1 = AQ1 = P1Q1. Hence ∆AP1Q1 is equilateral, and ∠AQ1P1 = 600.
Suppose P1 and Q1 drift away from the circle, and are at the points P&Q represented in the diagram. Then the value is definitely less than 600.
If P and Q are collinear with A, then the angle is 0(0).
So, the maximum value is 600, and minimum 0(0)
Answer : C
Answer: (C) Between 0 and 60
Question: Divide $2000 among B,C in the ratio 4:16. How many $ that C get?
(A) $1200
(B) $1400
(C) $1600
(D) $1800
(E) $2000
Rationale: Sum of ratio terms = 4+16 = 20
C = 2000*16/20 = $1600
Answer is C
Answer: (C) $1600