divelab/Sys2Bench huggingface dataset:
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
Options:
A)34
B)21
C)23
D)25
E)29
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer: C
Answer: C
Question: Dhoni bought 5 shirts with the average cost of $60. If David also buys the sixth shirt with the price of $ 72, what is the average (arithmetic mean) price of those 6 toys?
Options:
A)$63
B)$64
C)$65
D)$62
E)$66
Rationale: 5 shirts-> Total cost = 5 * Avg cost = 5*60 = 300
Sixth toy cost = 72
Total cost for 6 toys= 300+72 = 372
AM = 372/6= 62
Hence D
Answer: D
Question: How many natural numbers are there which give a remainder of 41 after dividing 1997?
Options:
A)2
B)4
C)6
D)None of these
E)Cannot be determined
Rationale: Solution
Let us assume that the quotient is Q and divisor is D.
Using the condition given in question,
1997 = QD + 41
⇒ QD = 1956.
Now we will factorize 1956 in two parts such that D (divisor) is more than 41. Answer C
Answer: C
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
Options:
A)600
B)700
C)800
D)900
E)1000
Rationale: Explanation:
(40/100) * X â€“ (20/100) * 650 = 190
2/5 X = 320
X = 800
ANSWER IS C
Answer: C
Question: A man spends Rs. 1400 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
Options:
A)2050
B)2100
C)2200
D)2300
E)2400
Rationale: Explanation:
Total expenditure for the first 3 months = 3 Ã— 1400 = 4200
Total expenditure for 4 months = 4 Ã— 1550 = 6200
Total expenditure for 5 months = 5 Ã— 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4200 + 6200 + 9000 + 5200 = Rs. 24600
So, Average monthly income = 25200/12 = Rs. 2050
Answer A
Answer: A
Question: A particular parking garage is increasing its rates by 15 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
Options:
A)10%
B)11%
C)12%
D)13%
E)14%
Rationale: Let parking rate = 100
=(15/100+15)*100
=13.04%
ANSWER:D
Answer: D
Question: Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $45,000 per year plus 20 percent commission for each sale made. If each of her sales is for $1,500, what is the least number of sales she must make per year if she is not to lose money because of the job change?
Options:
A)57
B)177
C)178
D)133
E)378
Rationale: Lets say she sales x items so her commission will be : x * 1500*20 /100 = 300x
Salary difference is: 85000 - 45000 = 40000
So commission must at least be equal to salary difference i.e. x = 40000/300= 133 (Approx).
Hence answer is C
Answer: C
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference V between the greatest and least of the five integers?
Options:
A)4K
B)4k^2 -4k
C)4-4k
D)4
E)4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference V= 10k - 3 - (10k - 7)
= 4
Answer - D
Answer: D
Question: A zinc-copper alloy with 3 kg of pure zinc would contain 80% of zinc. The alloy with 2 kg of 80% zinc alloy contains 64% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.
Options:
A)2.4 kg or 80%
B)1.4 kg or 88%
C)3.4 kg or 60%
D)7.4 kg or 18%
E)0.8 kg or 45.7%
Rationale: Right Answer Explanation:
x : 3
y : 100
80
20 : 80 – y
(80-y)/3 = 20/x = ………..(1)
In the second case,
x 2
y 80
64
16 64-y
Therefore (64-y)/2 = 16/x ………..(2)
Dividing (1) and (2)
=
640 – 8y = 960 – 15y
7y = 320
y = 45.7
x = 60/(80-45.7) = 60/34.3 = 1.75 kg
Quantity of zinc in x = 45.7% of x
= 0.457 1.75
= 0.799=0.8 kg
Weight and percentage of zinc is 0.8 kg or 45.7%
E
Answer: E
Question: Of the 200 math majors at a certain university, 20 percent will be assigned to advanced calculus on Monday and Wednesday and the remaining 70 percent will be assigned to advanced calculus on Tuesday and Thursday. However, 40 percent of the math majors prefer Tuesday and Thursday and 60 percent prefer Monday and Wednesday. What is the lowest possible number of math majors who will NOT be assigned to the days they prefer?
Options:
A) 15
B) 20
C) 30
D) 45
E) 60
Rationale: 30% of students are assigned to Monday and Wednesday = 0.3*200 = 60
70% of students are assigned to Tuesday and Thursday = 0.7*200 = 140
60% of students prefer Monday and Wednesday = 0.6*200 = 120
40% of students prefer Tuesday and Thursday = 0.4*200 = 80
Since we need theleastnumber of students who will not be assigned to their preferred days, we shall fit in themaximumpossible students as per their preference:
All of the 40% of students who prefer Tuesday and Thursday can be accommodated to their preferred days, whereas only 60 out of 120 students who prefer Monday and Wednesday can be accommodated to their preferred days.
The remaining 60 students who prefer Monday and Wednesday will be allocated to Tuesday and Thursday by default, which is not their choice.
Answer is B.
Answer: B
Question: A motorcyclist goes from Bombay to Pune, a distance of 160 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)2:5
C)1:4
D)1:1
E)1:6
Rationale: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2 = 5:2
Speed Ratio = 2:5
Answer: B
Answer: B
Question: According to a 2010 census, China's population was 1.34 billion people. If the ratio of male's to females is 1.052:1, respectively, then how many women are there? Answer in terms of (M = women).
Options:
A)W = M - 1.052
B)W = (M)(1.052)
C)W = M + 1.052
D)W = M/1.052
E)W = 1.052 - M
Rationale: The ratio of M to W, where
M = the number of males, and
W = the number of females.
Population = 1.34 billion people.
M/W:M/M = 1.052:1, so
M/W = 1.052
W = M/1.052
Answer is D
Answer: D
Question: A can do a piece of work in 28 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
Options:
A)5days
B)6days
C)7.5days
D)14days
E)9days
Rationale: Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =28∗1/2=14days
Option D
Answer: D
Question: A certain number when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: Explanation:
50 + 25 = 75/15 = 5 (Remainder)
B
Answer: B
Question: In the biology lab of "Jefferson" High School there are 5.4*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
Options:
A)100
B)200
C)500
D)1000
E)5000
Rationale: 5.4*10^6/ 10800==> 54*10^3/108==> 54000/108= 500
ANSWER:C
Answer: C
Question: The cost price of a radio is Rs.1900 and it was sold for Rs.1330, find the loss %?
Options:
A)18%
B)31%
C)30%
D)45%
E)12%
Rationale: 1900 ---- 570
100 ---- ? => 30%
Answer:C
Answer: C
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 10 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
Options:
A)11/3 DAYS
B)10/3 DAYS
C)12/3 DAYS
D)3/12 DAYS
E)3/10 DAYS
Rationale: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/5, B'S 1 DAY'S WORK = 1/10
(A+B)'S 1 DAY'S WORK = (1/5+1/10)=3/10=10/3
SO, A AND B TOGETHER CAN FINISH THE WORK IN 10/3 DAYS.
CORRECT OPTION: B
Answer: B
Question: In a simultaneous throw of pair of dice. Find the probability of getting the total more than 7.
Options:
A)5/19
B)5/12
C)5/28
D)5/10
E)5/11
Rationale: Explanation:
Here n(S) = (6 x 6) = 36
Let E = event of getting a total more than 7
= {(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
Therefore,P(E) = n(E)/n(S) = 15/36 = 5/12.
Answer: B) 5/12
Answer: B
Question: The price of 3 tables and 4 chairs is Rs. 3300. With the same money one can buy 2 tables and 10 chairs. If one wants to buy 1 table and 1 chair, how much does he need to pay?
Options:
A)940
B)1050
C)1100
D)1240
E)1296
Rationale: Let price of a table = t
and price of a chair = c
3t + 4c = 3300 ---(Equation 1)
2t + 10c = 3300
=> t + 5c = 1650 ---(Equation 2)
(Equation 2) × 3 => 3t + 15c = 4950 ---(Equation 3)
(Equation 3) - (Equation 1) => 11c = 1650
=> c = 150
Substituting the value of c in equation 1, we get
3t + (4 × 150) = 3300
=> 3t = 3300 – 600 = 2700
=>t = 2700/3 = 900
Cost of 1 table and 1 chair = c + t = 150 + 900 = 1050
Answer : Option B
Answer: B
Question: A train running at the speed of 180 km/hr crosses a pole in 7 seconds. What is the length of the train?
Options:
A)530
B)305
C)503
D)430
E)350
Rationale: Speed=(180 * 5/18) m/sec = (50) m/sec Length of the train = (Speed x Time) = (50 * 7) m
= 350 m.
Answer: E
Answer: E
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 16%?
Options:
A)20%
B)26%
C)42%
D)27%
E)22%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 84
2/3 SP1 = 84
SP1 = 126
100 --- 26 => 26%
Answer: B
Answer: B
Question: The arithmetic mean and standard deviation of a certain normal distribution are 12 and 1.2, respectively. What value is exactly 2 standard deviations less than the mean?
Options:
A)9.6
B)11
C)11.5
D)12
E)12.5
Rationale: Mean = 12
Two standard deviations is 1.2 + 1.2 = 2.4
There could be two calues for this.
Mean + two standard deviations = 14.4
Mean - Two standard deviations = 9.6
Answer choice has 9.6 and so A is the answer.
Answer: A
Question: If X is the sum of first 10 positive even integers and Y is the sum of first 10 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
A)10
B)25
C)50
D)75
E)100
Rationale: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 10 positive even integers minus the sum of first 10 positive odd integers will be 10.
Answer: A.
Answer: A
Question: Select Odd number:
6, 9, 15, 21, 24, 28, 30
Options:
A)20
B)21
C)24
D)28
E)30
Rationale: Each of the numbers except 28, is a multiple of 3.
answer D
Answer: D
Question: There is a 4 inch cube painted on all sides. This is cut into no of 1 inch cubes. What is the no of cubes which have no painted sides.
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The original cube is cut into 64 pieces. Removing all cubes from any two opposite pairs of faces leaves total 32 cubes, as one face contains 16 cubes each. It can be seen that in the remaining two layers, only four each from each layer have no sides painted. So total = 2*4=8 cubes.
ANSWER:B
Answer: B
Question: If m and n are positive integer, and 1800m=n^3, what is the least possible value of m?
Options:
A)2
B)3
C)15
D)30
E)45
Rationale: 1800*m=n^3
m=n^3/1800
=n^3/(3^2*5^2*2^3)
so n has to be 3*5*2 so that n^3 is divisible by 1800.
So m= (2*3*5)^3/(3^2*5^2*2^3)
m=15
ANSWER:C
Answer: C
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Options:
A)40/9 days
B)40/7 days
C)7.5 days
D)8.5 days
E)9.5 days
Rationale: A's one hour work = 1/8.
B's one hour work = 1/10.
(A+B)'s one hour work = 1/8+1/10 = 9/40.
Both A & B can finish the work in 40/9 days
Answer : A.
Answer: A
Question: The difference between the length and breadth of a rectangle is 42 m. If its perimeter is 280 m, then its area is:
Options:
A)1520 m2
B)4250 m2
C)4459 m2
D)4092 m2
E)None
Rationale: EXPLANATION
We have: (l â€“ b) = 42 and 2(l + b) = 280 or (l + b) = 140.
Solving the two equations, we get: l = 91 and b = 49.
Area = (l x b) = (91x 49) m2 = 4459 m2.
Answer C
Answer: C
Question: Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.00 at the candy store. What is this student’s weekly allowance?
Options:
A)$2.75
B)$3.25
C)$3.75
D)$4.25
E)$4.75
Rationale: Let x be the value of the weekly allowance.
(2/3)(2/5)x = 100 cents
(4/15)x = 100
x = $3.75
The answer is C.
Answer: C
Question: A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio W of milk and water in the resultant mixture?
Options:
A)17 : 3
B)9 : 1
C)3 : 17
D)5 : 3
E)11: 2
Rationale: he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.
Step 1.
When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.
Step 2.
When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.
Shortcut.
We are essentially replacing water in the mixture with pure milk.
Let W_o be the amount of water in the mixture originally = 8 litres.
Let W_r be the amount of water in the mixture after the replacements have taken place.
Then,{W_r}/{W_o}= (1-R/M)^n
where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.
Hence, {W_r}/{W_o} =(1/2)^2  =1/4
Therefore W,W_r ={W_o}/4= 8/4 = 2 litres.B
Answer: B
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
Options:
A)15
B)66
C)88
D)1
E)12
Rationale: 90 * 10/60 = 15 kmph
Answer: A
Answer: A
Question: A present value of a machine is $2500. Its value depletiation rate is 5% per annum then find the machine value after 2 years?
Options:
A)$2100
B)$2546
C)$2256
D)$2451
E)$2345
Rationale: P= $2500
R = 5%
T = 2 years
Machine value after 2 years = P[(1-R/100)^T]
=2500*19/20 * 19/20
=$2256 approximately
Answer is C
Answer: C
Question: Express the following as a fraction: 0.8%
Options:
A)1/8
B)8/10
C)8/100
D)4/5
E)None of the Above
Rationale: 0.8 =8/10 = 4/5
Answer is D.
Answer: D
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
Options:
A)287
B)2878
C)388
D)480
E)277
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
Answer:D
Answer: D
Question: A man bets on no. 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes?
Options:
A)23:2
B)35:1
C)37:13
D)39:11
E)41:11
Rationale: Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B)
Answer: B
Question: For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 6 minutes from 9:00 in the morning to 6:00 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 2 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
Options:
A)$23400
B)$25920
C)$28080
D)$28500
E)$29160
Rationale: From 9:00 in the morning to 6:00 in the afternoon, inclusive there are 9*10=90 five-minute intervals, thus total of 54*30 tickets were sold.
Say x student and 2x regular tickets were sold, then x+2x=90*30 --> x=30*30 and 2x=2*(30*30)=30*60.
Therefore, the total revenue from ticket sales that day was 30*30*6+30*60*10=$23,400.
Answer: A.
Answer: A
Question: If a Bus is travelling at a speed of 45 kmph, crosses a pole in 1 sec, then the length of train is?
Options:
A)12 m
B)12.3 m
C)12.5 m
D)12.8 m
E)13 m
Rationale: Explanation:
D = 45 * 5/18 * 1 = 12.5 m
Answer: Option C
Answer: C
Question: The front wheels of a wagon are 2Π feet in circumference and the rear wheels are 3Π feet in circumference. When the front wheels have made 10 more revolutions than the rear wheels, how many feet has the wagon travelled?
Options:
A)30Π
B)45Π
C)60Π
D)90Π
E)None
Rationale: Solution
Let the rear wheel make x revolutions. Then, the front wheel makes (x+10) revolutions.
(x+10) x 3Π = x×2Π
‹=›3x + 30 = 2x
‹=›x = 30.
Distance travelled by the wagon = (2Π x 30)ft
‹=›(60Π) ft.
Answer C
Answer: C
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
Options:
A)17/26
B)17/27
C)17/22
D)17/20
E)17/98
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: D
Question: If q = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =
Options:
A)-2
B)-1
C)0
D)2
E)None of the above
Rationale: Let us transform the formula:
q = (x – 5)² + (x +1)² – 6 =
x² – 10x + 25 + x² + 2x + 1 – 6 =
2x² – 8x + 20 = 2 × (x² – 4x + 10) =
2 × ((x² – 4x + 4) + 6) =
2 × ((x – 2)² + 6)
Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.
x – 2 = 0
x = 2
The correct answer is choice (D).
Answer: D
Question: Look at this series: 201, 202, 204, 207, ... What number should come next?
Options:
A)205
B)208
C)210
D)211
E)None
Rationale: Explanation: In this addition series, 1 is added to the first number; 2 is added to the second number; 3 is added to the third number; 4 is added to the fourth number; and go on.
Answer: Option D
Answer: D
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)1m
B)6m
C)9m
D)2m
E)8m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: D
Answer: D
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 13.69, the number of the member is the group is:
Options:
A)57
B)67
C)37
D)87
E)97
Rationale: Money collected =(13.69 x 100) paise = 1369 paise
numbers of members = 1369 squareroot = 37
Answer C
Answer: C
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio T of revenue from car sales in 1996 to revenue from truck sales in 1996?
Options:
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3
Rationale: A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2
Answer: A
Question: If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?
Options:
A)6
B)4
C)8
D)8
E)None of these
Rationale: 80 = 2 x 5 x 8
Since 653xy is divisible by 2 and 5 both, so y = 0.
Now, 653x is divisible by 8, so 13x should be divisible by 8.
This happens when x = 6.
x + y = (6 + 0) = 6.
Answer: A
Answer: A
Question: What is the product of the prime numbers between 1 and 7?
Options:
A)10^1
B)10^2
C)10^3
D)10^4
E)10^5
Rationale: C)
Answer: C
Question: A train 320 m long passed a pole in 28 sec. How long will it take to pass a platform 700 m long?
Options:
A)12 sec
B)59 sec
C)93 sec
D)89 sec
E)46 sec
Rationale: Speed = 320/28
= 11 m/sec.
Required time = (320 + 700)/11
= 92.7 sec.
Answer: C
Answer: C
Question: What is the dividend? Divisor is 0, the Quotient is 69, the remainder is 1.
Options:
A)2
B)69
C)0
D)4
E)1
Rationale: Dividend= Divisor * Quotient + Remainder
D= 0 * 69 + 1
D= 0 + 1
D=1
(e.g. Answer: E)
Answer: E
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)98%
B)20%
C)80%
D)90%
E)23%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: B
Question: m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 18) both lie on the line defined by the equation x = (y/6) - (2/5), what is the value of p?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: x = (y/6) - (2/5), and so y = 6x + 12/5. The slope is 6.
(n+18-n) / (m+p-m) = 6
p = 3
The answer is C.
Answer: C
Question: Three candidates contested an election and received 500, 7632 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
A)57%
B)60%
C)58.8%
D)90%
E)80%
Rationale: total votes are 19760 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*11628/19760 = 58.8%
ANSWER:C
Answer: C
Question: There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total T of the book?
Options:
A)3003
B)3027
C)3024
D)3021
E)3018
Rationale: First, you have to find the common ratio for all 3 books. You have:
P:C:B
3:2 --> multiply by 2 (gives you row 3)
4:6
6:4:3
Hence:
P:C:B:T(Total)T
6:4:3:13 ----> This means, the Total Number must be a multiple of 13.
Answer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Answer: A
Question: Ben likes long bike rides. On one ride, he goes biking for six hours. For the rst hour, he bikes
at a speed of 15 miles per hour. For the next two hours, he bikes at a speed of 12 miles per
hour. He remembers biking 90 miles over the six hours. Compute the average speed, in miles
per hour, Ben biked during the last three hours of his trip.
Options:
A)20
B)35
C)17
D)51
E)46
Rationale: Ben biked 90-15- 2 * 12 = 51 miles over the last three hours, averaging a speed of
51/3 = 17 miles per hour.
correct answer C
Answer: C
Question: The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet?
Options:
A)165
B)161
C)162
D)163
E)164
Rationale: To minimize one quantity maximize other.
164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165.
Answer: A.
Answer: A