divelab/Sys2Bench huggingface dataset:
Question: A man has Rs. 80 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)15
B)60
C)75
D)90
E)105
Rationale: Answer : A
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 80
16x = 80
x =5.
Hence, total number of notes = 3x = 15.
Answer: A
Question: (128.5 x 32) + (13.8 x 30) = ? x 25
Options:
A)524.48
B)556.02
C)574.36
D)181.04
E)595.46
Rationale: Explanation :
? = (128.5 x 32) + (13.8 x 30)/25
= 4112 + 414/25 = 181.04
Answer : Option D
Answer: D
Question: Two pipes A and B can fill a cistern in 37 ½ min and 45 minutes respectively. Both the pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after
Options:
A)6 minutes
B)9 minutes
C)45 minutes
D)3 minutes
E)4 minutes
Rationale: If pipe B is turned off after x mins, then
(2*30)/75 + x/45 =1
x/45 = 1-60/75 = 1/5
x= 45/5= 9 mins
ANSWER:B
Answer: B
Question: If a(a - 6) = 27 and b(b - 6) = 27, where a ≠ b, then a + b =?
Options:
A)−48
B)6
C)−2
D)46
E)48
Rationale: i.e. if a =-3 then b = 9
or if a = 9 then b =-3
But in each case a+b = -3+9 = 6
Answer: option B
Answer: B
Question: Nine persons went to a hotel for taking their meals. Eight of them spent 14 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?
Options:
A)115
B)117
C)119
D)122
E)135
Rationale: Let the average expenditure of all the nine be x.
Then, 14 × 8 + (x + 8) = 9x or 8x = 120 or x = 15.
∴ Total money spent = 9x = (9 × 15) = 135.
Answer E
Answer: E
Question: What is the greater of the two numbers whose product is 2048, given that the sum of the two numbers exceeds their difference by 64?
Options:
A)A)90
B)B)32
C)C)64
D)D)70
E)of these
Rationale: Let the greater and the smaller number be g and s respectively.
gs = 2048
g + s exceeds g - s by 64 i.e., g + s - (g - s) = 64
i.e., 2s = 64 => s = 32.
g = 2048/s = 64.
ANSWER:C
Answer: C
Question: For an upcoming charity event, a male vocalist has agreed to sing 5 out of 8 “old songs” and 3 out of 7 “new songs.” How many ways can the singer make his selection?
Options:
A)25
B)50
C)150
D)217.78
E)600
Rationale: =8C5*7C3
=8*7/3*7*5/3
=217.78
Ans = D
Answer: D
Question: On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
Options:
A)Saturday
B)Friday
C)Monday
D)Tuesday
E)Surday
Rationale: Explanation:
The year 2006 is an ordinary year. So, it has 1 odd day.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday
S0, 8th Dec, 2006 is Friday.
Answer: B) Friday
Answer: B
Question: [( 3.242 x 10 ) / 100] = ?
Options:
A)0.045388
B)4.5388
C)0.03242
D)473.88
E)None of these
Rationale: Answer
Multiplying 3.242 x 10=3.242
Now divide 3.242 by 100
So, 3.242 ÷ 100= 0.03242
∴ Shift the decimal two places to the left as 100
Correct Option: C
Answer: C
Question: Profit selling 10 candles equals selling price of 3 bulbs. While loss on selling 10 bulbs equal selling price of 4 candles. Also profit percentage equals to the loss percentage and cost of a candle is half of the cost of a bulb. What is the ratio of selling price of candles to the selling price of a bulb?
Options:
A)5:4
B)3:2
C)4:5
D)3:4
E)NONE
Rationale: Solution:
Price	Candle	Bulb
SP	A(let)	C(let)
CP	B	D
and, C = 2A
Profit = 10 (B-A) = 3D
Loss = 10 (C-D) = 4B
Profit % = (3D*100)/10A
Loss % = (4B*100)/10C
Now, By the questions,
(3D*100)/10A = (4B*100)/10C
B/D = 3/2.
Answer: Option B
Answer: B
Question: A room 3 m 21 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
Options:
A)27636
B)27640
C)27647
D)27713
E)27675
Rationale: Explanation:
Area of the room = (321 x 777) cm2.
Size of largest square tile = H.C.F. of 321 cm and 777 cm = 3 cm.
Area of 1 tile = (3 x 3) cm2.
Number of tiles required =(321×777)/(3×3)=27713
Answer: Option D
Answer: D
Question: Jill has 42 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
Options:
A)3
B)6
C)9
D)72
E)14
Rationale: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 42 1 3/4w = 42w=24The total number of jars = 3w =72Answer: D
Answer: D
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)21
B)25
C)20
D)29
E)24
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: C
Question: The greatest number of four digits which is divisible by 10, 20, 15 and 60 is:
Options:
A)9200
B)9300
C)9400
D)9600
E)9900
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 10, 20, 15 and 60 is 300.
On dividing 9999 by 300, the remainder is 99.
Required number (9999 - 99) = 9900.
ANSWER :E
Answer: E
Question: A,B,C invested the capitals in a business. If A invested Rs. 30,000 more thanC and B invested Rs.10,000 more than A, then how should a profit of Rs.15,000 be divided among A,B and C? Given : Capital of C is Rs.10,000
Options:
A)6000, 4500, 4500
B)6200, 5800, 3000
C)6000, 7500, 1500
D)6500, 5500, 3000
E)6000, 5250, 3750
Rationale: A==40,000
B==50,000
C==10,000
so, ration are 4:5:1
profit 15000
so,, 15000/10==1500
so,, A==6000, B==7500,, C==1500
ANSWER:C
Answer: C
Question: A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?
Options:
A)3 : 6
B)3 : 9
C)3 : 3
D)3 : 4
E)3 : 1
Rationale: Since S # 1/t
S1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4
Answer:D
Answer: D
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Options:
A)5 : 2
B)7 : 3
C)9 : 2
D)13 : 4
E)15 : 8
Rationale: Explanation:
Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40
x = 20.
Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
Answer: B
Answer: B
Question: What is the greatest positive integer T such that 3^T is a factor of 9^10?
Options:
A)5
B)T=9
C)T=10
D)T=20
E)30
Rationale: What is the greatest positive integer T such that 3^T is a factor of 9^10?
9^10 = (3^2)^10 = 3^20
D. 20
Answer: D
Question: A farmer had d animals, all of which the farmer bought for the same price. The farmer decided to sell the animals. 20 of the animals were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, the farmer made neither a profit nor a loss. Which of the following is equal to d?
Options:
A)24
B)26
C)28
D)30
E)36
Rationale: Let P be the price the farmer paid for each animal.
The total profit on the 20 animals is 20*0.1*P.
The total loss on the other (d-20) animals is (d-20)*0.2*P.
(d-20)*0.2*P = 20*0.1*P
0.2*d = 2 + 4
d = 30
The answer is D.
Answer: D
Question: A batsman in his 12th innings makes a score of 65 and thereby increases his average by 3 runs. What is his average after the 12th innings if he had never been ‘not out’?
Options:
A)32
B)43
C)44
D)45
E)46
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 3) + 65
∴ x = 32
Answer A
Answer: A
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)6.25
B)6.22
C)6.29
D)6.39
E)6.13
Rationale: Required run rate
= [282 - (3.2 * 10)]/40
= 250/40
= 6.25
Answer: A
Answer: A
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options:
A)2
B)7
C)5
D)6
E)8
Rationale: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5
Answer: C
Answer: C
Question: There were two candidates in an election. Winner candidate received 55% of votes and won the election by 100 votes. Find the number of votes casted to the winning candidate?
Options:
A)550
B)744
C)255
D)199
E)231
Rationale: W = 55% L = 45%
55% - 45% = 10%
10% -------- 100
55% -------- ? => 550
Answer:A
Answer: A
Question: A person invested in all 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is:
Options:
A)200
B)600
C)800
D)1200
E)None of these
Rationale: Let the parts be x, y and [2600 – (x + y)].Then,
x×4×1/100=y×6×1/100=[2600−(x+y)]×8×1/100
∴ y⁄x = 4⁄6 = 2⁄3 or y = 2⁄3x.
So, x×4×1100=[2600−53x]×8100x×4×1100=[2600−53x]×8100
⇒ 4x = (7800−5x)×8/3⇒52x=(7800×8)
⇒ x = (7800×8/52)=1200.
∴ Money invested at 4% = 1200.
Answer D
Answer: D
Question: There are 23 students in a class. In how many different ways can a committee of 3 students be formed?
Options:
A)1254
B)1482
C)1771
D)1875
E)1923
Rationale: 23C3 = 23*22*21 / 6 = 1771
The answer is C.
Answer: C
Question: What will come in place of the x in the following Number series? 2, 4, 8, x , 22
Options:
A)33
B)16
C)12
D)14
E)43
Rationale: (D)
The pattern is + 2, + 4, + 6, +8 â€¦â€¦â€¦..
So the missing term is = 8 + 6= 14
Answer: D
Question: A pair of articles was bought for $50 at a discount of 20%. What must be the marked price of each of the article?
Options:
A)$25
B)$31.25
C)$29.65
D)$35.95
E)$45.62
Rationale: S.P. of each of the article = 50/2 = $25
Let M.P = $x
80% of x = 25
x = 25*100/80 =$31.25
Answer is B
Answer: B
Question: The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg. What is the weight of the new person?
Options:
A)75 kg
B)85 kg
C)95 kg
D)65 kg
E)55 kg
Rationale: The total weight increase = (8 x 2.5) kg = 20 kg
weight of new person = (35 + 20) kg = 55 kg
The answer is E.
Answer: E
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
Options:
A)227
B)887
C)585
D)2679
E)27
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer:C
Answer: C
Question: In how many different ways can 3 boys and 3 girls sit on a bench such that the girls always sit together?
Options:
A)96
B)108
C)120
D)132
E)144
Rationale: We can think of the girls as one unit.
The number of ways to arrange 4 units in order is 4!
The girls can have different arrangements, so we multiply this by 3!
The number of ways to sit is 4!*3!=144
The answer is E.
Answer: E
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)2
B)8
C)9
D)6
E)4
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: B
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/45 hours
B)30/14 hours
C)37/13 hours
D)30/13 hours
E)30/19 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26
= 30/13 hours.
Answer: D
Answer: D
Question: Beth received 2/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 2/3 of the votes cast?
Options:
A)1/5
B)2/7
C)3/10
D)7/20
E)4/9
Rationale: Let the total votes be 100. Beth received 40 votes, other votes 100-40=60. In order to have received 1/2 of the votes she needed 200/3 votes so 80/3 more, which is 4/9 of the other votes.
Answer: E.
Answer: E
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
A)2 4/2 hours
B)2 1/2 hours
C)2 1/6 hours
D)2 1/1 hours
E)2 1/2 hours
Rationale: Required time
= (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer:E
Answer: E
Question: A 300 meter long train crosses a platform in 30 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)287m
B)278m
C)350m
D)200m
E)282m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 30
= 50/3
3(x + 300)
= 1500 è x
= 200m.
Answer:D
Answer: D
Question: Find the least number of complete years in which a sum of money put out at 15% compound interest will be more than double of itself?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: 5 years
Answer: A
Answer: A
Question: A baker filled with a measuring cup with 2/5 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
Options:
A)1/8 cup
B)3/8 cup
C)21/40 cup
D)1/2 cup
E)7/8 cup
Rationale: 2/5 is the original water in cup .half in batter.So left is 1/5 out which 1/8 is spilled out.So again left with 3/40.
so 50% more than what he started was =2/5+1/2*(2/5)=3/5
Amount of water needed to add = 3/5 - 3/40=21/40
C
Answer: C
Question: A man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
A)2.62
B)2.56
C)2.5
D)2.8
E)3.2
Rationale: Required time = (5 1/4)/3 + (5 1/4)/6 = 2.625 hours.
Answer:A
Answer: A
Question: do you know how many 2's are there between the terms 112 to 375?
Options:
A)A)156
B)B)157
C)C)158
D)D)159
E)E)160
Rationale: Let us calculate total 2's in the units place. (122, 132, 142 ... 192), (201, 212, 222, ... 292), (302, 312, ... 372) = 8 + 10 + 8 = 26
Total 2's in tenth's place, (120, 121, 122, ..., 129) + (220, 221, ..., 229) + (320, 321, ..., 329) = 30
Total 2's in hundred's place = (200, 201, ... 299) = 100.
Total 2's between 112 and 375 = 26 + 30 + 100 = 156
Answer:A
Answer: A
Question: The ratio between the present ages of P and Q is 5 : 8. After four years, the ratio between their ages will be 2 : 3. What is Q’s age at present?
Options:
A)36 years
B)20 years
C)24 years
D)Data inadequate
E)None of these
Rationale: P⁄Q = 5⁄8 or P = 5Q⁄8 .....(i)
P+4/Q+4=23
or, 3P + 12 = 2Q + 8 or, 2Q – 3P = 4... (ii)
Putting value of P from eq. (i),
2Q – 3 × 5⁄8Q = 4 ⇒ Q = 32
Answer E
Answer: E
Question: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Five years ago Jim was 5 times as old as Sam. How old is Jim now?
Options:
A)8
B)12
C)16
D)20
E)24
Rationale: We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 2 years younger than Fred
3) Five years ago, Jim was 5 times as old as Sam.
let's TEST Answer D: 20
IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 8 years old
5 years ago, Jim was 15 and Sam was 3, so Jim WAS 5 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
D
Answer: D
Question: A shopkeeper sold an article offering a discount of 10% and earned a profit of 25%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)39%
B)52%
C)15%
D)21%
E)28%
Rationale: Let C.P. be $100.
Then, S.P. = $ 125
Let marked price be $ x. Then, 90/100 * x = 125
x = 12500/90 = $ 139
Now, S.P. = $ 139, C.P. = Rs. 100
Profit % = 39%.
Answer: A
Answer: A
Question: A man purchased some fruits for Rs. 1000. He sold fruits worth 400 at 10% profit. At what profit per cent, must he sell the rest in order to gain 20% on the whole?
Options:
A)26(2/3)%
B)25%
C)30%
D)33(1/3)%
E)None
Rationale: Solution: To get 20 % profit on whole,
1000(CP)==20%(gain)==>1200(SP).
Total Profit = 1200 - 1000 = Rs. 200.
400 ==10%(gain)==>440.
He gets Rs. 40 profit on 400 hundred. Rest Profit = 200 - 40 = 160.
Then he must get Rs. 160 as profit on Rs. 600;
Hence, % profit = 160*100/600 = 26.66%.
Answer: Option A
Answer: A
Question: Find the volume , curved surface area and the total surface area of a cylinder with diameter of base 7 cm and height 40 cm.
Options:
A)952cm^2
B)957cm^2
C)954cm^2
D)958cm^2
E)None of them
Rationale: Volume = ∏r2 h = ((22/7)x(7/2)x(7/2)x40) = 1540 cm^3. .
Curved surface area = 2∏rh = (2x(22/7)x(7/2)x40)= 880 cm^2 .
Total surface area = 2∏rh + 2∏r2 = 2∏r (h + r)
= (2 x (22/7) x (7/2) x (40+3.5)) cm2
= 957 cm^2
Answer is B
Answer: B
Question: A thief is noticed by a policeman from a distance of 250 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
Options:
A)100
B)277
C)2987
D)150
E)271
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 250 - 100 = 150 m.
Answer: D
Answer: D
Question: Working simultaneously and independently at an identical constant rate, 20 machines of a certain type can produce a total of x units of product P in 4 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 8 days?
Options:
A)30
B)32
C)35
D)38
E)40
Rationale: The rate of 20 machines is rate=job/time=x/4 units per day --> the rate of 1 machine 1/20*(x/4)=x/80 units per day;
Now, again as {time}*{combined rate}={job done}
then 8*(m*x/80)=3x --> m=30.
Answer: A.
Answer: A
Question: (6+√3+√5)^2-(√3+√5)^2=?
Options:
A)1+2√3+2√5
B)36+12√3+12√5
C)1-√3+√5
D)1+√3-√5
E)√3+√5
Rationale: (6+√3+√5)^2-(√3+√5)^2
(6+√3)^2 + 5 +2 (6+√3) (√5) - ( 3 +5 + 2√3√5)
36+ 3+ 12√3 +5 +12 √5 + 2 √15 - 3-5 -2√15
36+12√3+12√5
B is the answer
Answer: B
Question: Two unbiased coins are tossed. Find the probability of getting two heads?
Options:
A)1/2
B)1/3
C)1/4
D)2/3
E)3/5
Rationale: S = {HH,HT,TH,TT}
E = Event of getting two heads
E = {TT}
P(E) = 1/4
Answer is C
Answer: C
Question: Find the odd man out. 742, 743, 633, 853, 871, 990, 532
Options:
A)532
B)990
C)633
D)742
E)871
Rationale: Explanation :
In all numbers except 742, the difference of third and first digit is the middle digit.
Answer : Option D
Answer: D
Question: The average monthly salary of 18 employees in an organisation is Rs. 2000. If the manager's salary is added, then the average salary increases by Rs. 200. What is the manager's monthly salary?
Options:
A)Rs.5800
B)Rs.3618
C)Rs.3600
D)Rs.3619
E)Rs.3610
Rationale: Manager's monthly salary
= Rs. (2200 * 19 - 2000 * 18)
=Rs.5800 Answer:A
Answer: A
Question: The area of a square is equal to nine times the area of a rectangle of dimensions 121 cm * 144 cm. What is the perimeter of the square?
Options:
A)1500 cm
B)1800 cm
C)1584 cm
D)1718 cm
E)1086 cm
Rationale: Area of the square = s * s = 9(121 * 144)
=> s = 3* 11 * 12 = 396 cm
Perimeter of the square = 4 * 396 = 1584 cm.
Answer: C
Answer: C
Question: (.24 x .35 ) / (.14 x .15 x .02) is equal to ?
Options:
A)2
B)20
C)200
D)2000
E)None of these
Rationale: Answer
(.24 x .35) / (.14 x .15 x .02)
= (24 x 35 x 100 ) / (14 x 15 x 2)
=200
Correct Option: C
Answer: C
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 50 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)21
B)88
C)45
D)99
E)22
Rationale: Relative speed = 50 + 30 = 80 km/hr.
80 * 5/18 = 200/9 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 9/200 = 45 sec
Answer: C
Answer: C
Question: A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 424. What is the sum of the last 8 of the even integers?
Options:
A)488
B)540
C)552
D)568
E)584
Rationale: Sum of n even consecutive integers = n(n+1)
Sum of 8 consecutive even integers that start at some point after n = (n+8)(n+9)
Given => (n+8)(n+9) - n(n+1) = 424
16n +72 = 424 - General equation for sum of consecutive 8 digits where n is where counting starts
Solving we get n = 22 (Where the count starts)
Sum of 8 consecutive integers after n = 22 will be count starting at n1 = 22+8 = 30
So Answer = 16*30 +72 = 552
ANSWER:C
Answer: C
Question: In an election, candidate A got 70% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.
Options:
A)330000
B)340000
C)347000
D)333200
E)357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 70 %
Therefore, the number of valid votes polled in favour of candidate A = 70 % of 476000
= 70/100 × 476000
= 33320000/100
= 333200
D)
Answer: D
Question: If 80 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Options:
A)10%
B)(8) 20%
C)30%
D)50%
E)55%
Rationale: I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?
20% appeared in the exam; however did not answer Question AQuestion B correctly
So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose
I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.
Now,
100 - [(80 - x) + x + (55 - x)] = 20 .......... values are in percent
x = 20 - 100 + 135
x = 55
Ans: E
Answer: E
Question: For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 2835 what is the least possible value of k?
Options:
A)5
B)7
C)9
D)11
E)13
Rationale: 2835 = 3*3*3*3*5*7
Thus k must include numbers at least up to the number 9 so that there are at least four appearances of 3 (that is: 3, 6, and 9=3*3).
The answer is C.
Answer: C
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent E of thatbeforeJuly 1 last year?
Options:
A)90%
B)99%
C)100%
D)101%
E)110%
Rationale: the total number of employees = n
the average salary = x
total salary to all emplyoees = xn
after
the total number of employees = n - 0.1n = 0.9n
the average salary = x + 10% of x = 1.1x
total salary to all emplyoees = 0.9n (1.1x)
total salary after as a % of total salary before E = [0.9n (1.1x)]/xn= 0.99 or 99%=B
Answer: B
Question: An exam paper consists of 5 problems, each problem having 3 internal choices. In how many ways can a candidate attempt one or more problems?
Options:
A)1020
B)1023
C)1030
D)1054
E)1060
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
B
Answer: B
Question: A 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Options:
A)286 m
B)350 m
C)277 m
D)400 m
E)267 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/42 = 50/3
x = 400 m.
Answer:D
Answer: D