mathewhe/aqua_rat huggingface dataset:
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
(A) 12
(B) 45
(C) 77
(D) 88
(E) 51
Rationale: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3)
= 45 kmph.
Answer: B
Answer: (B) 45
Question: In the following alphabet second half is written first and then the first half is arranged in reverse order.
Then which of the following will be the 5th letter to the left of 16th letter from the right?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
(A) S
(B) Y
(C) U
(D) H
(E) K
Rationale: N O P Q R S T U V W X Y Z M L K J I H G F E D C B A
(16 + 5) = 21th letter from your right is S.
Answer: A
Answer: (A) S
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more?
(A) 49
(B) 40
(C) 21
(D) 79
(E) 27
Rationale: 760 ---- 22
760 ---- 20
x ----- 19
x*19 = 760*20
x = 800
760
-------
40
Answer: B
Answer: (B) 40
Question: The sum of two numbers is 90 and their difference is 10. Find their product.
(A) 104
(B) 2000
(C) 315
(D) 325
(E) 335
Rationale: Let the numbers be x and y.
Then x + y = 90 and x - y = 10
x = 50; y = 40
xy = 50 * 40 = 2000
ANSWER:B
Answer: (B) 2000
Question: If |4x+6| = 36, then find the sum of the values of x?
(A) -3
(B) 4
(C) 3
(D) -5
(E) 6
Rationale: |4x+6| = 36
4x+6 = 36 or 4x+6 = -36
4x = 30 or 4x = -42
x = 7.5 or x = -10.5
sum = 7.5-10.5 = -3
Answer is A
Answer: (A) -3
Question: A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 10 months and 7 months respectively. What was the ratio of their investments?
(A) 10:12:14
(B) 12:24:28
(C) 20:22:12
(D) 25:49:80
(E) None of these
Rationale: Explanation :
Ratio in which A,B and C shared the profit = 5 : 7 : 8
Assume that the ratio of their investment = a:b:c
Then 14a : 10b : 7c = 5 : 7 : 8
Good to go, we got the equation. Now it's a matter of time to find a, b and c
14a/10b = 5/7
=> 98a = 50b
=> b = 98a/50 = 49a/25 ---(1)
14a/7c =5/8
=> 2a/c =5/8
=> 16a = 5c
=> c = 16a/5 ---(2)
a : b : c = a : 49a/25 : 16a/5 = 1 : 49/25 : 16/5 = 25 : 49 : 80. Answer : Option D
Answer: (D) 25:49:80
Question: 1,3,5,7,9,..50 find term of sequnce for this?
(A) 1235
(B) 1540
(C) 1650
(D) 2000
(E) 2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500
E
Answer: (E) 2500
Question: The population of a village is 6000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?
(A) 5000
(B) 4860
(C) 5400
(D) 4800
(E) 5120
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
6000 Ã— 90/100 Ã— 90/100 = 4860
B
Answer: (B) 4860
Question: If u+5/v is a prime integer, which of the following must be true?
1.v=5u
2. v is a prime integer
3. u+5/v is ODD.
(A) None
(B) 1 only
(C) 2 only
(D) 1 and 2 only
(E) 2 and 3 only.
Rationale: I would pick up numbers and do .
i hope the question is (u+5)/v....
let u = 3 , v = 4
3+5/4 = 2 = Prime
1. v is not equal to 5u
2.v is not a prime number
3. (u+5)/v is not odd.
hence A
Answer: (A) None
Question: There are between 110 and 120 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
(A) 111
(B) 113
(C) 115
(D) 117
(E) 119
Rationale: The numbers with the form 4n+1 are 113 and 117.
Only 113 has the form 3k+2.
The answer is B.
Answer: (B) 113
Question: A one-foot stick is marked in 1/4 and 1/5 portion. How many total markings will there be, including the end points?
(A) 18
(B) 16
(C) 13
(D) 9
(E) 11
Rationale: LCM of 20 = 20
1/4 marking are (Table of 5) 0...... 5 ......10..... 15......20
(Total = 5)
1/5 marking are (Table of 4) 0 ....... 4 ...... 8...... 12........ 16......20 (Total = 6)
Overlapping markings are 0 ........ 20 (Total = 2)
Total markings = 5+6-2 = 9
Answer = D
Answer: (D) 9
Question: Beth received 4/12 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?
(A) 1/5
(B) 2/7
(C) 3/10
(D) 7/20
(E) 2/8
Rationale: Let the total votes be 12. Beth received 2 votes, other votes 12-4=8. In order to have received 1/2 of the votes she needed 6 votes so 2 more, which is 2/8 of the other votes.
Answer: E.
Answer: (E) 2/8
Question: The sum of a rational number and its reciprocal is 13/6. Find the number.
(A) 4/3 or 3/4
(B) 0
(C) 1/3 or 3
(D) 2/3 or 3/2
(E) 2
Rationale: Let the number be x.
Then, x + (1/x) = 13/6 => (x2 + 1)/x = 13/6 => 6x2 – 13x + 6 = 0
=> 6x2 – 9x – 4x + 6 = 0 => (3x – 2) (2x – 3) = 0
	x = 2/3 or x = 3/2
Hence the required number is 2/3 or 3/2.
Answer is D.
Answer: (D) 2/3 or 3/2
Question: A baseball card decreased in value 60% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
(A) 28%
(B) 30%
(C) 32%
(D) 36%
(E) 64%
Rationale: Let the initial value of baseball card = 100
After first year , value of baseball card = (1- 60/100)* 100 = 40
After second year , value of baseball card =(1 - 10/100)* 40 = 36
total percent decrease of the card's value over the two years = (100-36)/100 *100%
=64%
Answer E
Answer: (E) 64%
Question: The average of 11 numbers is 10.6. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 9
(B) 9.2
(C) 10
(D) 14.8
(E) 16
Rationale: Explanation:
1 to 11 = 11 * 10.6 = 116.6
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 116.6 = 14.8
6th number = 14.8
D)
Answer: (D) 14.8
Question: Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each?
(A) 6, 4
(B) 5, 2
(C) 2, 5
(D) 7, 3
(E) 3, 7
Rationale: Explanation:
Let the present ages of Anand and Bala be 'a' and 'b' respectively.
Given a - 2b = 1 --- (1)
a+b = 7----(2) =>b =7-a
Substituting b = 7-a in first equation,
3a-14 = 1 => a = 5
=> b = 2
Answer: B
Answer: (B) 5, 2
Question: A man can row upstream at 35 kmph and downstream at 45 kmph, and then find the speed of the man in still water?
(A) 32 kmph
(B) 34 kmph
(C) 40 kmph
(D) 45 kmph
(E) 65 kmph
Rationale: US = 35
DS = 45
M = (35 + 45)/2 = 40
Answer:C
Answer: (C) 40 kmph
Question: which of the following is equivalent to (1-cos^2θ)/cos^2θ
(A) cos^2θ
(B) sin^2θ
(C) tan^2θ
(D) sec^2θ
(E) None
Rationale: cos 2θ = cos2 θ − sin2 θ = 2 cos2 θ − 1=1 − 2 sin2 θ
tan^2θ
C
Answer: (C) tan^2θ
Question: The average (arithmetic mean) of the even integers from 0 to 120 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 60 inclusive?
(A) 10
(B) 15
(C) 20
(D) 30
(E) 60
Rationale: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 120 is 120/2 = 60
The average of the even numbers from 0 to 60 is 60/2 = 30
The answer is D.
Answer: (D) 30
Question: A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 66 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
(A) A.138
(B) B.50
(C) C.48
(D) D.46
(E) E.44
Rationale: At 6:00 it'll chime 6 times. If we assume that the time taken to chime is x, then time between chimes is also x. So you have 6 chimes, which is 6x and 5 time intervals between chimes. This means that 11x = 66 seconds. Thus x = 6 seconds.
By a similar logic, at 12:00, there are 12 chimes and 11 intervals so the total time is (12+11)x = 23x = 138 seconds.
Answer A
Answer: (A) A.138
Question: The sum of three consecutive even numbers is 246. What are the numbers?
(A) 80,82,84
(B) 65,68,71
(C) 45,47,42
(D) 100,102,49
(E) 87,88,89
Rationale: First x Make the first x
Second x+2 Even numbers, sowe add 2 to get the next
Third x+4 Add 2more (4 total) to get the third
F +S +T =246 SummeansaddFirst (F)plusSecond(S)plusThird(T)
(x)+(x+2)+(x+4)=246 Replace each F , S, and T withwhatwe labeled them
x+x+2+x+4=246 Here the parenthesis are not needed
3x+6=246 Combine like terms x+x+x and 2+4
−6 −6 Subtract 6 fromboth sides
3x=240 The variable ismultiplied by 3
3 3 Divide both sides by 3
x=80 Our solution for x
First 80 Replace x in the origional listwith 80.
Second (80)+2=82 The numbers are 80, 82, and 84.
Third ( 80)+4=84
correct answer A
Answer: (A) 80,82,84
Question: 0,1,2,0.5,2,3,5,1,2,0,2,1,4,2,3,?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: take first four digits from series: 0,1,2,0.5
0+1=1,1/2=0.5
2,3,5,1
2+3=5,5/5=1
2,0,2,1
2+0=2,2/2=1
4,2,3,?
4+2=6,6/3=2
ANSWER:D
Answer: (D) 2
Question: A fraction in reduced form is such that when it is squared and then its numerator is reduced by 33(1/3)% and denominator is reduced to 20%, its result is twice the original fraction. The sum of numerator and denominator is:
(A) 8
(B) 13
(C) 17
(D) 15
(E) None of these
Rationale: Solution: Let the fraction be x/y.
When fraction is squared its numerator is reduced by 33(1/3) and denominator is reduced by 20%.
According to question,
(x/y)2 * 33(1/3)%/20% = 2(x/y).
Or, (x/y)2 * (2/3)/(1/5) = 2(x/y).
Or, x/y = 3/5. Sum of numerator and denominator is,
(x+y) = 3+5
= 8.
Answer: Option A
Answer: (A) 8
Question: A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 6 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
(A) 0.5< t < 1.5
(B) 1.75< t < 2.0
(C) 2.0 < t < 2.5
(D) 2.5 < t < 3.0
(E) 3 < t < 3.5
Rationale: D=2, and R=1
circumference thus is 2pi miles
we know that she walked 6mph
knowing the formula rt=D, we can deduce that t= D/r
D is 2pi miles and r is 6mph
t = 2pi/6
pi can be rewritten as 22/7
2*22/7 = 44/7 and multiply this by 1/6 = 44/42. This is greater than 0.5, but less than 1.5, therefore, 0.5<t<1.5. Answer choice A.
Answer: (A) 0.5< t < 1.5
Question: It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
(A) 30 days
(B) 23 days
(C) 45 days
(D) 54 days
(E) 76 days
Rationale: One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)
The total no. of days required to complete the work
= (75 * 20) / 50 = 30
Answer:A
Answer: (A) 30 days
Question: Yesterday's closing prices of 2,640 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
(A)  484
(B)  726
(C)  1,100
(D)  1,320
(E)  1,440
Rationale: Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 2640 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1)(2) to get H = 1440.
E is my answer.
Answer: (E)  1,440
Question: Rahul went to a shop and bought things worth Rs. 26, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) Rs 15
(B) Rs 12.10
(C) Rs 20.70
(D) Rs 16.80
(E) None of these
Rationale: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 26 - 5 - 0.30
=20.70
Answer : C
Answer: (C) Rs 20.70
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 30 ways
(B) 40 ways.
(C) 50 ways.
(D) 60 ways.
(E) 70 ways.
Rationale: Explanation:
The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
A)
Answer: (A) 30 ways
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:
(A) 5336
(B) 5340
(C) 5342
(D) 5345
(E) 5356
Rationale: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336.
A
Answer: (A) 5336
Question: A, B and C invested Rs.6000, Rs.4000 and Rs.10000 respectively, in a partnership business. Find the share of A in profit of Rs.11000 after a year?
(A) 3300
(B) 1100
(C) 2667
(D) 600
(E) 4000
Rationale: Explanation:
6000:4000:10000
3:2:5
3/10 * 11000 = 3300
Answer: A
Answer: (A) 3300
Question: a,b,c,d,e are distinct numbers. if (75-a)(75-b)(75-c)(75-d)(75-e)=2299 then a+b+c+d= ?
Hint:2299 is divisible by 11.
(A) 292, 306, 270, 282, 289
(B) 292, 306, 270, 282, 280
(C) 292, 306, 270, 282, 2228
(D) 292, 306, 270, 282, 212
(E) 292, 306, 270, 282, 210
Rationale: 2299 = 11×11×19×1×1=11×−11×19×−1×1=11×11×19×1×1=11×−11×19×−1×1=
Two of the terms in the given expression should equal to 1. As all the digits are distinct, two of the terms should be negative.
One possible solution = (75 - 64)(75 - 56)(75 - 86)(75 - 74)(75 - 76)
Then a + b + c + d + e = 64 + 56 + 86 + 74 + 76 = 356
But as the sum of only 4 terms was asked, we have to subtract one term.
So given answer can be one of 292, 306, 270, 282, 280
Answer:B
Answer: (B) 292, 306, 270, 282, 280
Question: The yearly compensation of salesperson Y is $4,000 plus 8 percent of the amount by which the total value of the items sold by the store exceeds $250,000. The yearly compensation of salesperson Z is 12 percent of the amount by which the total value of the items sold by the store exceeds $300,000. In the previous year, both salesperson Y and salesperson Z had the same compensation. What was the yearly compensation of salesperson Y last year?
(A) $18,000
(B) $21,000
(C) $24,000
(D) $30,000
(E) $50,000
Rationale: Compensation of Y is same as Compensation of Z. Therefore 12/100 (total sales) = one of the answers
=> Total sales = 100/12* (one of the answers). Now it is given that the sales of of Z should be greater than 300K for getting the 12% compensation
All the values except (E) 50K give total sames less than 300K. Hence answer is E.
Answer: (E) $50,000
Question: If A takes x days to do a work then B takes 2x days to do the same work then with in how many day's A will alone complete this work ?
(A) 27
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: 1/x+1/2x = 1/18 = > 3/2x = 1/18 = > x = 27 days. Hence, A alone can finish the work in 27 days.
Answer:A
Answer: (A) 27
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
(A) 2888
(B) 3000
(C) 2887
(D) 27781
(E) 2788
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer: B
Answer: (B) 3000
Question: How many seconds will a 250 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 12
(B) 30
(C) 40
(D) 15
(E) 60
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 250 * 3/50 = 15 sec.
Answer: Option D
Answer: (D) 15
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) 129
(B) 287
(C) 189
(D) 188
(E) 112
Rationale: Explanation:
CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
Answer:C
Answer: (C) 189
Question: If the sum of two numbers is 45 and the L.C.M and sum of the reciprocal of the numbers are 120 and 11/120 then HCF of numbers is equal to:
(A) 55
(B) 5
(C) 10
(D) 45
(E) 4
Rationale: Let the numbers be a and b and HCF is x,
Then, a + b = 45 and ab = x * 120 = 120x
Required sum = 1/a + 1/b = (a + b)/ab = 45/120x = 11/120.
x=5.
ANSWER:B
Answer: (B) 5
Question: Find the product of the localvalue and absolutevalue of 7 in 20768?
(A) 9200
(B) 1100
(C) 4900
(D) 3200
(E) 1600
Rationale: Local value of 7 = 7 x 100 = 700
Place value of 7 = 7
There fore = 7 x 700 = 4900
C
Answer: (C) 4900
Question: If 23m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
(A) 2m −1
(B) 4m
(C) 6m
(D) m/5
(E) 8m
Rationale: 23m - n = p
Add n to both sides:
23m = n + p
Add m to both sides:
24m = n + p + m
Now, divide both sides by 3
8m = (n + p + m)/3 = the average of n, p, and m
E
Answer: (E) 8m
Question: Find the odd man out. 187, 264, 346, 473, 682, 781
(A) 187
(B) 346
(C) 781
(D) 682
(E) 473
Rationale: In all numbers except 346, the middle digit is the sum of other two digits.Answer is B
Answer: (B) 346
Question: There are 1000 military people in a division of the army. There is one Officer for every 24 soldiers in that division. Now the question is how many officers are in the division?
(A) 22
(B) 35
(C) 40
(D) 73
(E) 75
Rationale: C
40
24 soldiers + 1 officer makes a group of 25 people. Now number of such groups = 1200/25 = 40.
Answer: (C) 40
Question: 8^b + 8^b + 8^b + 8^b + 8^b + 8^b + 8^b + 8^8 =
(A) 7^b
(B) 8^(b + 1)
(C) 7^(7b)
(D) 8^b
(E) 49^B
Rationale: Easy one.
8*8^b = 8^(b+1)
Ans. B
Answer: (B) 8^(b + 1)
Question: If 4/p=8 & 4/q=18 then p-q=?
(A) 5/18
(B) 6/24
(C) 7/24
(D) 8/24
(E) 9/24
Rationale: p=4/8 , q=4/18=>q=2/9
therefore
p-q=(1/2)-(2/9)=5/18
ANSWER:A
Answer: (A) 5/18
Question: If (x^2 + 3x - 10)/4≤ x + 1, then x could be represented by which of the following?
(A) − 4 ≤ x ≤ − 3
(B) − 4 ≤ x ≤ 3
(C) − 3 ≤ x ≤ 3
(D) 3 ≤ x ≤ 4
(E) − 3 ≤ x ≤ 4
Rationale: IMO E is correct answer
solving through eqautions
x^2 +3x-10<= 4x+4
(x+3)(x-4)<=0
Answer: (E) − 3 ≤ x ≤ 4
Question: Seven different objects must be divided among three persons. In how many ways this can be done if at least one of them gets exactly one object.
(A) 223
(B) 776
(C) 287
(D) 196
(E) 211
Rationale: Division of m+n+p objects into three groups is given by (m+n+p)!m!×n!×p!(m+n+p)!m!×n!×p!
But 7 = 1 + 3 + 3 or 1 + 2 + 4 or 1 + 1 + 5
So The number of ways are (7)!1!×3!×3!×12!(7)!1!×3!×3!×12! + (7)!1!×2!×4!(7)!1!×2!×4! + (7)!1!×1!×5!×12!(7)!1!×1!×5!×12! = 70 + 105 + 21 = 196
Answer:D
Answer: (D) 196
Question: How many four letter combinations can be formed using the letters of the word MISTY?
(A) 15
(B) 80
(C) 120
(D) 180
(E) 240
Rationale: The number of letters in the given word is five.
The number of four letter combinations that can be formed using these five letters is
= 5 * 4 * 3 * 2 = 120.
Answer: C
Answer: (C) 120
Question: The G.C.D. of 1.08, 0.36 and 0.9 is:
(A) 0.03
(B) 0.9
(C) 0.18
(D) 0.108
(E) None
Rationale: EXPLANATION
Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
Answer C
Answer: (C) 0.18
Question: 45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 45 meters deep by working for 6 hours?
(A) 25
(B) 35
(C) 45
(D) 55
(E) 65
Rationale: 45 workers * 8 hours / 30 meters = x * 6 / 45
x = 90 total workers
90 - 45 = 45 new workers
The answer is C.
Answer: (C) 45
Question: Carmelo and LeBron participate in a eight-person footrace on the basketball court during All-Star Weekend. If all eight contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
(A) 20160
(B) 2520
(C) 720
(D) 120
(E) 42
Rationale: 8! = 40320
40320/2=20160 half the time carmelo is in front, vice versa
Answer:
(A) 20160
Answer: (A) 20160
Question: Find the value of x from this equation? 7(x - 1) = 21
(A) 1
(B) 2
(C) 4
(D) 5
(E) 6
Rationale: 1. Divide both sides by 7:
2. Simplify both sides:
x - 1 = 3
3. Add 1 to both sides:
x - 1 + 1 = 3 + 1
4. Simplify both sides:
x = 4
C
Answer: (C) 4
Question: Jim wishes to buy 3 gifts that cost 19 dollars, 9 dollars, and 12 dollars. He has 1/4 of the money
he needs. How much more money must he earn in order to buy the gifts?
(A) $57
(B) $47
(C) $7
(D) $30
(E) $27
Rationale: $19 + $9 + $12 = $40 needed
1/4 x $40 = $10 on hand
$40 - $10 = $30 to earn
correct answer D
Answer: (D) $30
Question: A taxi charges v dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.
(A) vn – c/8(100)
(B) cv + 4n-8/200
(C) v + (4cn-8c)/100
(D) v + 100cn/4
(E) 4cv(n-2) – 100
Rationale: This is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost v is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost v, or subtract the additional cost from v. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C).
Answer: (C) v + (4cn-8c)/100
Question: If x and y are even integers, which of the following is an odd integer?
(A) x-y
(B) x-y+2
(C) xy+2
(D) x-y-2
(E) none of these
Rationale: even - even = even
even + even = even
Answer :E
Answer: (E) none of these
Question: A student needs 60% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 40 marks, find the maximum marks set for the test.
(A) 180
(B) 200
(C) 220
(D) 240
(E) 260
Rationale: 60% = 120 marks
1% = 2 marks
100% = 200 marks
The answer is B.
Answer: (B) 200
Question: If anangletis defined as 1 percent of 1 degree, then how many anglets are there in a third circle?
(A) 0.36
(B) 3.6
(C) 12,000
(D) 3,600
(E) 36,000
Rationale: 1 degree * 1/100 = 1 anglet
So 1 degree = 100 anglets
=> 120 degrees = 12000 anglets
Answer - C
Answer: (C) 12,000
Question: In a division sum, the remainder is 8 and the divisor is 6 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is:
(A) 110.6
(B) 129.5
(C) 130.5
(D) 86
(E) 88
Rationale: Diver = (8*3)+3=27
6* Quotient = 27
Quotient = 4.5
Dividend = (Divisor * Quotient) + Remainder
Dividend = ( 27 * 4.5) + 8 = 129.5
B
Answer: (B) 129.5