divelab/Sys2Bench huggingface dataset:
Question: Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the number
Options:
A)5
B)15
C)7.5
D)4
E)16
Rationale: Explanation:
Let the number be x.
7x -15 = 2x + 10 => 5x = 25 => x = 5
Answer: Option A
Answer: A
Question: By selling 18 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)8
B)9
C)7
D)12
E)4
Rationale: 80% --- 18
120% --- ?
80/120 * 18 = 12
Answer: D
Answer: D
Question: A machine puts c caps on bottles in m minutes. How many Q hours will it take to put caps on b bottles?
Options:
A)60bm/c
B)Q=bm/60c
C)bc/60m
D)60b/cm
E)b/60cm
Rationale: The machine puts c caps in m minutes or c caps in m/60 hours.
Rate = c/m/60 = 60c/m.
To put b caps the machine will take:-
Time = Work/Rate
T = b/60c/m = bm/60c
Answer is B.
Answer: B
Question: Of the students at a certain high school, 100 percent took a course in algebra or geometry and 20 percent took courses in both. If the percent of students who took a course in algebra was 2 times the percent of students who took a course in geometry, what percent of the students took a course in algebra but not geometry?
Options:
A)50%
B)60%
C)45%
D)40%
E)35%
Rationale: You can also just use the formula
n(A or B) = n(A) + n(B) - n(A and B)
100 = 2X + X - 20
X = 40
2X = 80
This is the number of people who took algebra including those who took both. To get the number of people who took only algebra, 80 - 20 = 60%
Answer (B)
Answer: B
Question: The radius of a semi circle is 3.1 cm then its perimeter is?
Options:
A)15.94
B)12.41
C)16.1
D)32.92
E)32.3
Rationale: 36/7 r = 6.3 = 15.94
Answer:A
Answer: A
Question: I chose a number and divide it by 6. Then I subtracted 189 from the result and got 3. What was the number I chose?
Options:
A)1200
B)1152
C)1189
D)1190
E)100
Rationale: Let x be the number I chose, then
x/6−189=3
x/6=192
x=1152
Answer is B.
Answer: B
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 69 hats in this group, how many of these hats are not blue?
Options:
A)28
B)42
C)48
D)64
E)76
Rationale: B:G:P = 7:4:12 --> total of 23 parts.
Not blue = (G + P)/(total)*92 = 16/23*69 = 48.
Answer: C.
Answer: C
Question: Find the compound interest on Rs. 25000 in 2 years at 4% per annum. The interest being compounded half yearly.
Options:
A)Rs 2060.808
B)Rs 2060.801
C)Rs 2060.804
D)Rs 2060.802
E)Rs 2060.805
Rationale: Explanation:
Given:
Principal = Rs. 25000, Rate = 4 % per half year, Time = 2 years = 4 half years
Therefore,
Amount = P( 1 + (R/2)/100)2n
Amount = Rs. [25000*(1+ 2/100)4] = Rs. (25000 * 51/50*51/50*51/50* 51/50)
= Rs. 27060.804
Therefore,
C.I. = Rs. ( 27060.804 – 25000)
= Rs 2060.804
ANSWER: C
Answer: C
Question: Choose the missing terms out of the given alternatives.
BXJ, ETL, HPN, KLP, ?
Options:
A)MHQ
B)MIP
C)NIR
D)NHR
E)HEW
Rationale: D
NHR
The first, second and third letters move three steps forward, four steps backward and two steps forward respectively.
Answer: D
Question: In how many ways 4 boys and 4 girls can be seated in a row so that boys and girls are alternate?
Options:
A)1152
B)1987
C)2012
D)1856
E)2546
Rationale: number of ways = 2*4!*4! = 1152
Answer is A
Answer: A
Question: The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 5 seconds than it was moving after 3 seconds?
Options:
A)4
B)9
C)15
D)20
E)63
Rationale: Given: z=s^2+2s for 0≤s≤7
z(3) = 3^2 + 2*3 = 15
z(5) = 5^2 + 2*5 = 35
Therefore z(7) - z(3) = 35 - 15 = 20 km/hr
Option D
Answer: D
Question: A college starts from 10 AM continues till 1:30 PM. In this duration there are five periods. If 5 minutes are provided before each period to leave the room and enter the other, then what is the duration of each period?
Options:
A)38 min
B)41 min
C)40 min
D)42 min
E)52 min
Rationale: before first period no need to leave the room and enter the room.
so,for 5 periods 4 times 5 minutes break will be provided. that is 20 mins.
10 A.M-1:30 P.M=210mins
210-20=190
therefore 190/5=38 mins.
ANSWER:A
Answer: A
Question: John has taken four (4) tests that have an average of 90. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
Options:
A)81
B)90
C)82
D)94
E)97
Rationale: Traditional Method:
Total scored till now 90*4=360
Total score to avg 87 in 6 tests = 87*6=522
Total to be scored on 2 tests = 522-360=162
Avg on 2 tests = 162/2 = 81
Answer: A
Answer: A
Question: If 2x + y = 7 and x + 2y = 10, then (x + y)/3 =
Options:
A) 1
B) 4/3
C) 17/9
D) 18/5
E) 4
Rationale: We have two equations:
2x + y = 7
x + 2y = 10
Notice that something nice happens when we ADD them. We get:
3x + 3y = 17
Divide both sides by 3 to get:x + y = 17/3
So, (x + y)/3 =17/9
Answer: C
Answer: C
Question: A man buys an article for $20. and sells it for $25. Find the gain percent?
Options:
A)25%
B)50%
C)20%
D)15%
E)30%
Rationale: C.P. = $20
S.P. = $25
Gain = $5
Gain% = 5/20 *100 =25%
Answer is A
Answer: A
Question: The distance between Delhi and Mathura is 185 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Options:
A)10.50 a.m.
B)11.40 a.m.
C)10.30 a.m.
D)11.50 a.m.
E)1.40 a.m.
Rationale: D = 185 â€“ 20 = 165
RS = 20 + 25 = 45
T = 165/45 = 3 2/3 hours
8 a.m. + 3 hrs 40 min = 11.40 a.m.
ANSWER:B
Answer: B
Question: A car runs at the speed of 50 km per hour when not serviced and runs at 60 kmph when serviced. After servicing the car covers a certain distance in 6 hours. How much time will the car take to cover the same distance when not serviced?
Options:
A)8 hours 12 minutes
B)6 hours 15 minutes
C)8 hours 15 minutes
D)7 hours 12 minutes
E)None
Rationale: Explanation :
Time = 60*6 / 50 = 7 hours 12 mins
Answer – D
Answer: D
Question: Answer: Option D
Explanation:
Options:
A)11 3/3
B)11 3/8
C)11 3/2
D)11 3/7
E)11 3/1
Rationale: (x – 5)/15 + x/20 = 1
x = 11 3/7 days
Answer: D
Answer: D
Question: A train 300 m long, running with a speed of 54 km/hr will pass a tree in?
Options:
A)17 sec
B)16 sec
C)20 sec
D)14 sec
E)12 sec
Rationale: Speed =54 * 5/18
= 15 m/sec
Time taken = 300 * 1/15
= 20 sec
Answer: C
Answer: C
Question: A fort of 3000 soldiers has provisions for 75 days. After 15 days some of them left and the food was now enough for the same period of 75 days as before. How many of them left?
Options:
A)500
B)550
C)600
D)650
E)700
Rationale: 2000 ---- 50
3000 ---- 60
x ----- 75
x*75 = 3000*60
x=2400
3000
-------
600
Answer: C
Answer: C
Question: P can do a certain work in 9 days. Q is 60% more efficient than P. How many days does Q alone take to do the same job?
Options:
A)60/9
B)45/8
C)30/7
D)25/6
E)18/4
Rationale: Each day, P can do 1/9 of the work.
Each day, Q can do 1.6/9 of the work = 16/90 of the work
The time taken by B alone to complete the total work is 90/16 = 45/8 days.
The answer is B.
Answer: B
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 26,000 is made?
Options:
A)328897
B)122000
C)877888
D)277768
E)188871
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 26,000 is made = 96,000 + 26,000 = Rs. 1,22,000
Answer: B
Answer: B
Question: The L.C.M. of two numbers is 60. The numbers are in the ratio 2 : 3. Then sum of the number is:
Options:
A)28
B)32
C)40
D)53
E)50
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 60 or x = 10.
The numbers are 20 and 30.
Hence, required sum = (20 + 30) = 50.
Answer: Option E
Answer: E
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=13. What is the value of f(6)?
Options:
A)-1
B)0
C)1
D)2
E)4
Rationale: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=13 then f(5)=13-5=8 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=8-6=2.
Answer: D.
Questions on funtions to practice:
Answer: D
Question: The sum of the present ages of a father and his son is 57 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:
Options:
A)17
B)18
C)19
D)20
E)21
Rationale: Let the present ages of son and father be x and (57 - x) years respectively.
Then, (57 - x) - 6 = 4(x - 6)
51 - x = 4x - 24
x = 15
The son's age after 6 years will be 21.
The answer is E.
Answer: E
Question: Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ?
Options:
A)6000
B)5400
C)6200
D)7200
E)8200
Rationale: Investment Ratio = Profit Sharing Ratio.
Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6.
Giri share =
13200
× 6 / 11 = Rs.7200
Hari share =
13200 × 5 / 11 = Rs.6000
Option A
Answer: A
Question: If mno < 0 and no > 0, which of the following must be positive?
Options:
A) xy
B) xz
C) (m^2)no
D) m(n^2)o
E) xy(z^2)
Rationale: Given that no is positive and mno is negative, you can say that m MUST be negative. As for n and o either they are both positive or both negative.
Option (C) has m^2 which is positive and no which is positive. So (C) must be positive.
Answer: C
Question: The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
Options:
A)58
B)70
C)63
D)65
E)72
Rationale: 1/2bh=1/2(2a+1)(2a+6)
Now 4a-2=2a+6
2a=8 . a=4
Therefore,
A(0,0); B(0,14); C(9,14)
1/2*9*14=63
Answer: C
Answer: C
Question: On increasing the price of T.V. sets by 60%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
Options:
A)4
B)5
C)56
D)28
E)7
Rationale: Explanation:
Let the price be = Rs.100, and number of units sold = 100
Then, sale value = Rs.(100 × 100) = Rs.10000
New sale value = Rs.(160 × 80) = Rs.12800
Increase% = 2800/10000 × 100 = 28%
Answer: D
Answer: D
Question: A box contains SEVEN bulbs out of which 3 are defective. If THREE bulbs are chosen at random, find the probability that atleast one bulb is good?
Options:
A)32/33
B)35/36
C)37/39
D)34/39
E)34/35
Rationale: Required probability= 1- 3C3/7C3= 1 - 1/35= 34/35Answer:E
Answer: E
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?
Options:
A)2 1/4
B)3 1/4
C)4 1/3
D)6 1/2
E)8 1/2
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
ANSWER A
Answer: A
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
Options:
A)5/5
B)5/9
C)5/3
D)5/2
E)5/1
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Answer: B
Question: A watch passes through three hands and each person gains 25%. If the third person sells it for $312.50, what did the first person pay for it?
Options:
A)$148
B)$152
C)$156
D)$160
E)$164
Rationale: 1.25*1.25*1.25 * original price = 312.5
(5/4)^3 * original price = 312.5
original price = 64*312.5 / 125 = $160
The answer is D.
Answer: D
Question: Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 6 hours?
Options:
A)675
B)750
C)1,800
D)1,350
E)7,500
Rationale: 8 machines/ 360 cans = 5 machines/ x cans
8x= 1800
x=225
(225)(6 hours)= 1350 cans. The answer is D.
Answer: D
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)Rs.500
B)Rs.1190
C)Rs.1200
D)Rs.163
E)Rs.897
Rationale: Explanation:
S.P. = 85% of Rs. 1400 = Rs(85/100*1400)=Rs.1190
ANSWER:B
Answer: B
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 51. What is that number
Options:
A)4
B)10
C)12
D)14
E)15
Rationale: Explanation:
=> 3(2x+9) = 51
=> 2x+9 = 17
=> x = 4
Answer: Option A
Answer: A
Question: 8 years ago there were 5 members in the Arthur's family and then the average age of the family was 36 years. Mean while Arthur got married and gave birth to a child. Still the average age of his family is same now. What is the age of his wife at the time of his child's birth was.If the difference between the age of her child and herself was 26 years?
Options:
A)16 years
B)26 years
C)36 years
D)66 years
E)86 years
Rationale: Since we know that the difference b/w the age of any two persons remains always constant, while the ratio of their ages gets changed as the time changes.
so, if the age of his child be x (presently)
Then the age of wife be x + 26 (presently)
Thus the total age = x + ( x + 26) = 32 [\inline \because 252-220 =32]
Rightarrow x = 3
age of her child is 3 years and her self is 29 years. Hence her age at the time of the birth of her child was 26 years.
Answer: B
Answer: B
Question: What percent of a day is 8 hours?
Options:
A)12%
B)12.5%
C)33.3%
D)11.3%
E)None of these
Rationale: Explanation :
Solution: required percentage = (8/100 * 24) = 33.3%
Answer : C
Answer: C
Question: A new savings account offers 7 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?
Options:
A)$80.00
B)$84.40
C)$360.00
D)$6,360.00
E)$6,427.35
Rationale: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.07) (1/2) = $210. (Note: the 6 months are “1/2” in the equation since 6% is a yearly rate, not a bi-yearly one).
Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,210. The interest earned during the final 6 months of the year is $6,210(.07)(1/2) = $217.35. Therefore, the total balance is the original amount ($6000) + $210 + $217.35 = $6,427.35.
The correct answer is E.
Answer: E
Question: One used-car salesperson receives a commission of $ 600 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
Options:
A)$ 5,000
B)$ 6,000
C)$ 8,000
D)$ 10,000
E)$ 12,000
Rationale: This question can be solved by TESTing THE ANSWERS.
We're given the pay rate of two different salespeople who sell cars:
1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price.
2) A straight commission of 6 percent of the car’s final sale price.
We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?
Let's TEST Answer B: $6,000
1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400
2nd salesperson = .06(6,000) = $360
These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...
Let's TEST Answer C: $8,000
1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480
2nd salesperson = .06(8,000) = $480
These totals are the SAME, so this must be the answer.
Final Answer:
E
Answer: E
Question: In how many ways can the letters C, A, A, R, W, A be arranged so that the three A's are not next to each other?
Options:
A)36
B)48
C)72
D)96
E)128
Rationale: 1 C
3 A
1 R
1 W
Number of ways these letters can be arranged = 6!/3! (3! to account 3 same As) = 120
Consider 3 As as 1 entity and thus the number of arrangements for (AAA)CRW = 4! = 24
Total allowed cases = 120-24 =96
D is the correct answer.
Answer: D
Question: Which of the following is NOT a prime number?
Options:
A)21
B)31
C)41
D)11
E)51
Rationale: Ans is A
A prime number has itself and 1 as the only factors. e.g. 2, 3, 7, 11, 19. Factors of 21 = {1 , 3 , 7 , 21} => 21 is not a prime number
Answer: A
Question: If 4 men working 10 hours a day earn Rs. 600 per week, then 9 men working 6 hours a day will earn how much per week?
Options:
A)Rs 840
B)Rs 320
C)Rs 810
D)Rs 680
E)None of these
Rationale: Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 600 : x
hence 4 * 10 *x = 9 * 6 * 600
or x = 9*6*600/ 4*10 = 810
Answer : C
Answer: C
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?
Options:
A)18:11
B)18:18
C)18:10
D)18:12
E)18:14
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
Question: Two vertical ladders length of 6 m and 11 m are kept vertically at a distance of 12 m. Find the top distance of both ladders?
Options:
A)22
B)27
C)13
D)19
E)17
Rationale: So distance between the top points = AD = 122+52−−−−−−−√=13122+52=13
So in paper B he did well.
Answer:C
Answer: C
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 7th position from either end of the row.
Can you find out how many girls are practicing together?
Options:
A)4
B)9
C)13
D)16
E)18
Rationale: As judith is 7th from either end of the row, it means that 6 girls are on one of her sides and 6 are present on the other.
6 + 6 + 1(judith herself) = 13.
Hence, 13 girls are practicing the dance together.
correct answer is C)13
Answer: C
Question: If a shoppkepper has two type of rice. One at Rs 50/- and another at Rs 80/- . He mixed the rice at 2:1 ratio. Find the average price of the mixture.
Options:
A)75
B)65
C)60
D)50
E)55
Rationale: Ratio = 2x:x, Total quantity=50*2x+80*x=180x
Average price=180x/(2x+x)=60
ANSWER:C
Answer: C
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 480 m, its area is?
Options:
A)150
B)240
C)277
D)261
E)281
Rationale: 5x + 12x + 13x = 480 => x = 16
a = 80, b = 192, c = 208
S = (80 + 192 + 208)/2 = 240
Answer: B
Answer: B
Question: Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter?
Options:
A)20
B)25
C)30
D)35
E)40
Rationale: For these type of questions, use the formula 7x/4 =[sum of ages] where x is the age of elder.
2)7x/3 = [sum of ages] whr x is the age of younger. Here peter is elder is 7x/4=35. Solve you get x= 20
ANSWER:A
Answer: A
Question: Tom wants to buy items costing $25.35, $80.69, and $85.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour.
Options:
A)8 hours
B)48 hours
C)38 hours
D)18 hours
E)33 hours
Rationale: $6.50 x .10 = $.65 is 10% of his hourly income
$6.50 - .65 = $5.85 hourly amount available to spend
$25.35 + $80.69 + $85.96 = $192 total needed
$192 ÷ $5.85 = 32.8... rounds to 33 hours
correct answer E
Answer: E
Question: If a number p is prime, and 2p+4 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 1/6 = 0.1666666... (a repeating pattern one digit long)
A
Answer: A
Question: The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?
Options:
A)4.5
B)4.6
C)4.7
D)4.8
E)None of the above
Rationale: Sum of the remaining two numbers
= (3.95 × 6) – [(3.4 × 2) + (3.85 × 2)]
= 23.70 – (6.8 + 7.7)
= 23.70 – 14.5 = 9.20
∴ Required average = (9.2⁄2) = 4.6
Answer B
Answer: B
Question: If A got 60 marks and B got 30 marks, then what percent of A's mark is B's mark?
Options:
A)A)60%
B)B)80%
C)C)65%
D)D)50%
E)of these
Rationale: A's marks = 60 ; B's marks = 30.
Let x% of A = B => x/100 * 60 = 30
=> x = (30 * 100)/60 = 50
B's marks is 50% of A's marks.
ANSWER:D
Answer: D
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
Options:
A)1677
B)1683
C)2523
D)3363
E)6546
Rationale: L.C.M. of 5, 6, 7, 8 = 840. Required number is of the form 840k + 3 Least value of k for which (840k + 3) is divisible by 9 is k = 2. Required number = (840 x 2 + 3) = 1683. Answer : B
Answer: B
Question: How many 6 letter words ( with or without meaning) can be formed using all the following 5 letters U,P,Q,R,S,and T so that letter P is to the left of letter R?
Options:
A)160
B)400
C)300
D)360
E)320
Rationale: Two positions can be selected out of 5 positions in 6C2 ways = 15 ways.
And the remaining 4 letters can be placed in 4 posions in 4! Ways = 24 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 4 letters can be arranged
Final Answer = 24 x 15 = 360 ways
D
Answer: D
Question: A train after traveling 50 kms from A meets with an accident and proceeds at 4/5th of the former speed and reaches B, 45 min late. Had the accident happened 20 kms further on, it would have arrived 12 mins sooner. Find the original speed and the distance.
Options:
A)5 hrs 30 mins
B)5 hrs 33 mins
C)5 hrs 36 mins
D)4 hrs 33 mins
E)6 hrs 33 mins
Rationale: speed = 25 kmph and distance = 125 kms.
scheduled time = 5 hrs.
Time taken in first case = 50/25 + 75/20 = 2+3.75 hrs = 5.75 hrs = 5 hrs 45 min
in second case, time taken = 70/25 + 55/20 = 111/20 hrs = 5 hrs 33 mins
ANSWER:B
Answer: B
Question: How long does a train 110 m long traveling at 36 kmph takes to cross a bridge of 170 m in length?
Options:
A)28
B)16.0
C)16.4
D)16.8
E)16.1
Rationale: D = 110 + 170 = 280 m
S = 36 * 5/18 = 10
T = 280 * 1/10 = 28 sec
Answer: A
Answer: A
Question: A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 yellow jellybeans; these jellybeans are the only items in the bag. If a person reaches into the bag and picks out only purple jellybeans, how many jellybeans would the person have to pick out in order to double the probability that a jellybean picked out of the bag at random would be a green jellybean?
Options:
A)5
B)15
C)19
D)24
E)25
Rationale: Chances of picking a green at present = 15 / (26 + 15 + 9) = 15/50 = 3/10
So required is double that chance = 2 * 3/10 = 3/5
since only purple are removed, the new count be x, 3/5 = 15 (x + 15 + 9)
solving for x gives x = 1.
So 26 -1 = 25 purple jellybeans needs to be removed.
Answer is E
Answer: E
Question: Carmelo and LeBron participate in a nine-person footrace on the basketball court during All-Star Weekend. If all nine contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
Options:
A)504020
B)181440
C)720
D)120
E)42
Rationale: 9! = 362880
362880/2=181440 half the time carmelo is in front, vice versa
Answer:
(B) 181440
Answer: B