divelab/Sys2Bench huggingface dataset:
Question: The average age of a group of persons going for picnic is years. Eighteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
Options:
A)5
B)10
C)18
D)32
E)50
Rationale: Solution
Let the initial number of persons be x. Then
16x + 18 x 15 = 15.5(x+20)
= 0.5x = 9
x =18.
Answer C
Answer: C
Question: In case L is the only individual sewing on committee B, which among the following shouldserve on committee A?
Options:
A)V and U
B)V and T
C)U and S
D)M and N
E)T and U
Rationale: M and N should serve on A
ANSWER:D
Answer: D
Question: There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 2 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
Options:
A)1/2
B)2/3
C)32/35
D)11/12
E)13/14
Rationale: answer is E
Total probability=8C3=56
4C3 +4C2*4C1+4C1*4C2=4+24+24=52
therefore the probability that at least one of the fashion magazines will be selected= 52/56=13/14
E
Answer: E
Question: At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 2 years?
Options:
A)4 %
B)7.14 %
C)2 6/7 %
D)5 %
E)6 %
Rationale: Explanation:
250 = (1750x2xR)/100
R = 7.14 %
Answer: Option B
Answer: B
Question: Pencils, Pens and Exercise books in a shop are in the ratio of 10: 2 : 3. If there are 120 pencils, the number of exercise books in the shop is:
Options:
A)26
B)36
C)46
D)56
E)66
Rationale: Explanation:
Let Pencils = 10x, Pens = 2x & Exercise books = 3x. Now, 10x = 120 hence x = 12.
Number of exercise books = 3x = 36.
Answer: B
Answer: B
Question: In Town P, 70 percent of the population are employed, and 21 percent of the population are employed males. What percent of the employed people in Town P are females?
Options:
A)46%
B)52%
C)58%
D)64%
E)70%
Rationale: The percent of the population who are employed females is 70-21 = 49%
The percent of employed people who are female is 49% / 70% = 70%.
The answer is E.
Answer: E
Question: What is the diffference between the place value and face value of 8 in the numeral 8635?
Options:
A)7992
B)7892
C)7792
D)7692
E)7982
Rationale: place value of 8 = 8 * 1000 = 8000
face value of 8 = 8
8000 - 8 = 7992
A
Answer: A
Question: A meeting has to be conducted with 3 managers. Find the number of ways in which the managers be selected from among 6 managers, if 2 managers will not attend the meeting together?
Options:
A)18
B)20
C)16
D)22
E)24
Rationale: we can either choose all 3 people from 4 manager who have no problems or choose 2 from the 4 and 1 from the 2 managers who have a problem sitting together
so 4C3 + (4C2 * 2C1)
this is 4 + 12=16
Answer : C
Answer: C
Question: If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
Options:
A)32
B)45
C)36
D)64
E)48
Rationale: Explanation :
The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.The first 24 of these words will start with A.Then the 25th word will start will CA _ _ _.The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.The next word starts with CH and then A, i.e., CHA _ _.The first of the words will be CHAMS. The next word will be CHASM.Therefore, the rank of CHASM will be 24+6+2= 32
Answer : A
Answer: A
Question: The bankers discount of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time is Rs. 30. The sum due is:
Options:
A)140
B)150
C)160
D)170
E)180
Rationale: Sum = (B.D*T.D)/(B.D-T.D)
(36*30)/36-30;
180
ANSWER:E
Answer: E
Question: Two pipes can fill a tank in 20 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
Options:
A)5 Hours
B)7 Hours
C)8 Hours
D)9 Hours
E)12 Hours
Rationale: In 1 hour it fill 1/20 + 1/12 - 1/20 = 1/12
So fill tank fill up in 12 Hours
ANSWER:E
Answer: E
Question: The volumes of two cones are in the ratio 1 : 30 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)6:5
B)6:9
C)6:2
D)2:2
E)2:8
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r1^2 . h1/r2^2. h2 => 1/30
= (1)^2h1/(2)^2h2
=> h1/h2 = 6/5
i.e. h1 : h2 = 6:5
Answer: A
Answer: A
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 1512 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
Options:
A)140
B)240
C)340
D)440
E)540
Rationale: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(1512-9-90*2)/3=540
Answer : E
Answer: E
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
Options:
A)$1
B)$1.84
C)$1.96
D)$2
E)$2.5
Rationale: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Answer: B
Question: How many total numbers of not more than 20 digits that can be formed by using the digits 0, 1, 2, 3, and 4 is
Options:
A)5 20
B)5 20 – 1
C)5 20 + 1
D)6 20
E)None of these
Rationale: Number of single digit numbers = 5
Number of two digits numbers = 4 × 5
∵ [0 cannot occur at first place and repetition is allowed]
Number of three digits numbers
= 4 × 5 × 5 = 4 × 5(2)
.... .... .... ....
.... .... .... ....
Number of 20 digits numbers = 4 × 5(19)
∴ Total number of numbers
= 5 + 4.5 + 4.5(2) + 4.5(3)........4.5(19)
= 5 + 4⋅5(519−1)5−14⋅5(5[19]−1)5−1 = 5 + 5(20) - 5 = 5(20)
Answer A
Answer: A
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
Options:
A)1/126
B)1/129
C)1/122
D)1/124
E)1/123
Rationale: Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄
= 1/126
Answer:A
Answer: A
Question: In a particular 100 meter race, 9 athletes are participating that are numbered 1-9. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?
Options:
A)102,330
B)115,990
C)132,220
D)152,770
E)181,440
Rationale: The total number of ways for the athletes to finish is 9! = 362,880.
#4 will be ahead of #2 in exactly half of these possibilities.
362,880/2 = 181,440
The answer is E.
Answer: E
Question: In an exam, Gibi scored 59 percent, Jigi scored 55 percent , Mike scored 99 percent and Lizzy 67 percent. The maximum score awarded in the exam is 700. Find the average mark scored by all the four students?
Options:
A)471
B)490
C)480
D)453
E)456
Rationale: Average mark scored by all the three boys =
[59/100 (700) + 55/100 (700) + 99/100 (700)+ 67/100 (700)] / 4
(413+385+693+469)/4= 490
Answer: B
Answer: B
Question: If S is the sum of the reciprocals of the consecutive integers from 61 to 70, inclusive, which of the following is less than S?
I. 1/6
II. 1/7
III. 1/8
IV .1/6>S >1/7
Options:
A)I
B)II
C)IV
D)III
E)I&II
Rationale: Since we summarize the reciprocals from 70 to 61, we can say also that we add ten numbers who are all (with one exception 1/70) greater than 1/70, so that the sum must be greater than 1/6.
On the other side we can say that we add the reciprocals from 61 to 70, so that the sum has to be less than the sum of ten times 1/61.
sum has to be greater than 1/7 and less than 1/6
C
Answer: C
Question: A rectangular plot 15 m × 10 m, has a path of grass outside it. If the area of grassy pathway is 54 m2, find the width of the path.
Options:
A)4 m
B)3 m
C)2 m
D)1 m
E)None of these
Rationale: Let the width of the path = W m
then, length of plot with path = (15 + 2W) m
and breadth of plot with path = (10 + 2W) m
Therefore, Area of rectangular plot (without path)
= 15 × 10 = 150 m2
and Area of rectangular plot (with path)
= 150 + 54 = 204 m2
Hence, (15 + 2W) × (10 + 2W) = 204
⇒ 4W2 + 50W – 54 = 0
⇒ 2W2 + 25W – 27 = 0
⇒ (W – 2)(W + 27) = 0
Thus W = 2 or –27
∴ with of the path = 2 m
Answer C
Answer: C
Question: Two trains of length 120 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Options:
A)100/7 sec
B)80/7 sec
C)57/7 sec
D)120/7 sec
E)104/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (120 + 100 + 300)/35
= 520/35 = 104/7 sec.
ANSWER:E
Answer: E
Question: If six persons sit around a table, the probability that some specified three of them are always together is
Options:
A)1/20
B)3/10
C)1/5
D)4/5
E)3/5
Rationale: There are six persons and three of them are grouped together. Since it is a circle, this can be done in 3! 3! ways.
Therefore, P = 3!3!/5 = 3/10
ANSWER:B
Answer: B
Question: What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?
Options:
A)1108
B)1683
C)2007
D)3363
E)3567
Rationale: LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9.
If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9.
If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9.
Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.
Answer: Option B
Answer: B
Question: (3x + 2) (2x - 7) = ax^2 + kx + n . What is the value of a - n + k ?
Options:
A)3
B)8
C)9
D)10
E)11
Rationale: Expanding we have 6x^2 - 21x + 4x -14
6x^2 - 17x - 14
Taking coefficients, a = 6, k= -17, n = -14
Therefore a - n + k = 6 - (-14) - 17 = 20 - 17 = 3
The answer is A.
Answer: A
Question: Pradip spends 40 per cent of his monthly income on food items, and 50 per cent of the remaining on clothes and conveyance. He saves one-third of the remaining amount after spending on food, clothes and conveyance. If he saves 19,200 every year,what is his monthly income?
Options:
A)24,000
B)12,000
C)16,000
D)20,000
E)None of these
Rationale: Food items = 40%
Clothes + conveyance = 1⁄2 of 60% = 30%
1⁄3 of 30% = 19,200⁄12 ⇒ 10% = 1600
∴ 100% = 16,000
Answer C
Answer: C
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)A)Rs.180
B)B)Rs.200
C)C)Rs.250
D)D)Rs.280
E)E)Rs.300
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
Option 'C'
Answer: C
Question: The average of 9 observations was 9, that of the 1st of 4 being 10 and that of the last 4 being 8. What was the 5th observation?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 1 to 9 = 9 * 9 = 81
1 to 4 = 4 * 10 = 40
4 to 9 = 6 * 8 = 48
5th = 48 + 40 =88 – 81 = 7
ANSWER:D
Answer: D
Question: A student has got marks in five subjects in the ratio 2:3:4:5:6 .The maximum marks of subjects in same sequence are in ratio 6:5:8:4:7.Total percentage of marks scored by him is 48%.FInd the maximum percentage obtained by him in a subject..
Options:
A)65
B)78
C)96
D)90
E)95
Rationale: lets marks obtain 2x,3x,4x,5x,6x.
total marks 6y,5y,8y,4y,7y.
addition of marks obtain=(2x+3x+4x+5x+6x)=20x
addition of total marks=(6y+5y+8y+4y+7y)=30y
so percentage=(20x/30y)*100
(20x/30y)*100=48
so,x/y=18/25
as we observed 5x/4y is the maximum marks
so 5x/4y=5/4*18/25*100=90%
ANSWER:D
Answer: D
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
Options:
A)1/3
B)2/5
C)3/7
D)8/27
E)9/29
Rationale: Total number of balls = (8 + 7 + 6) = 21.
E = event that the ball drawn is blue.
n(E) = 7
P(E) =n(E)/n(S) =7/21 = 1/3
ANSWER A
Answer: A
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 63 kmph?
Options:
A)22 sec
B)77 sec
C)25 sec
D)14.3 sec
E)17 sec
Rationale: D = 100 + 150 = 250
S = 63 * 5/18 = 17.5 mps
T = 250/17.5 = 14.3 sec
Answer:D
Answer: D
Question: If (5^15)(9^8)=3(15^x), what is the value of x?
Options:
A) 7
B) 9
C) 11
D) 13
E) 15
Rationale: (5^15)(9^8)=3(15^x)
=> 5^15 * 3^16 = 3 * 3^x * 5^x
=> 5^15 * 3^16 = 3^(x+1) * 5^x
Value of x = 15
Answer E
Answer: E
Question: In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability E this college graduate has a graduate degree?
Options:
A)1/11
B)1/12
C)1/13
D)3/19
E)3/43
Rationale: In believe the answer is D. Please see below for explanation.
0) we are told the following ratios
CGD - College Graduate with Degree
NCG - Non College Graduate
CGN - College Graduate no Degree
CGD NCG CGN
1 8
3 2
In order to make CGD and CGN comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get
CGD NCG CGN
3 24 16
If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?
Nr of CGD = 3
Nr of CG = 3+ 16 = 19
Probability E of CGD / (CG) -> 3/19
Answer D
Answer: D
Question: Sunil invested $ 1600 fir 3 years and $ 1100 for 4 years at the same rate of Simple Interest. If the total interest from these investments is $ 506, what is the rate of interest?
Options:
A)2 3/4%
B)5 1/3%
C)5 1/2%
D)6%
E)3 2/4%
Rationale: (1600x3xR)/100+(1100x4xR)/100=506
92R=506
R= 5 1/2%
Answer is C
Answer: C
Question: An article costing rs.200 is sold at 25% discount on a mark-up price. What is the selling price after
discount?
Options:
A)106
B)150
C)126
D)136
E)146
Rationale: 200*75/100=150
ANSWER:B
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58 ?
Options:
A)Rs. 3942
B)Rs. 3288
C)Rs. 3944
D)Rs. 3122
E)Rs. 3911
Rationale: Explanation:
Let the side of the square plot be 'a' ft.
Given area of the plot (a x a) = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 x 58 = Rs. 3944.
Answer: C
Answer: C
Question: A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length of the train (in metres) is:
Options:
A)188
B)176
C)175
D)96
E)None of these
Rationale: Explanation:
Let the length of train be L m.
Acc. to question
(264+L)/20 = L/8
2112+8L=20L
L= 2112/12 = 176 m
Answer B
Answer: B
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)Either ;30:1
B)Either ;35:1
C)12;7:1
D)12;72:1
E)16;22:14
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: Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles?
Options:
A)Six hours and 30 minutes
B)Seven hours and 30 minutes.
C)Eight hours and 20 minutes.
D)Nine hours and 15 minutes
E)Ten hours and 20 minutes
Rationale: Answer is B: Seven hours and 30 minutes.
since they are travelling towards each other, the total speed is 50 mph + 50*0.88 = 94 mph (0.88 since, the other car is 12% less than first one)
Distance to be covered is 705, so time taken = distance/speed = 705/94 = 7.5 hours or 7 hours and 30 mins.
ANSWER:B
Answer: B
Question: The sum of three integers A, B and C is 360. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
Options:
A)211
B)212
C)213
D)214
E)210
Rationale: A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=360
so 1/3(B+C)+B+C=360
4(B+C)/3= 360
B+C =360*3/4 = 270
A=360-270=90
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=360
so 1/5(A+C)+A+C=360
A+C=360*5/6=300
but A=90, so C=300-90=210
Answer :E
Answer: E
Question: A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many U apples did each person get before 45 people joined the feast?
Options:
A)20.
B)21.
C)22.
D)23.
E)24.
Rationale: Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13.
Since number of apples per person * total persons U= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C
Answer: C
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3680. They completed the work in 3 days with the help of C. How much is to be paid to C?
Options:
A)s. 380
B)s. 600
C)s. 460
D)s. 400
E)s. 480
Rationale: Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3680 × (1/8) = 460
Answer : Option C
Answer: C
Question: If 5 toys cost Rs, 234, what do 35 toys cost?
Options:
A)1645
B)1564
C)1546
D)1638
E)None of them
Rationale: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
= x=(35 X 234)/5 =1638
Answer is D
Answer: D
Question: At a supermarket, the ratio of the number of shampoos to the number of soaps is 8 to 5, and the ratio of the number of drinks to the number of shampoos is 3 to 4. If the ratio of the soaps to the number of cereals is 9 to 2, what is the ratio of the number of drinks to the number of cereals?
Options:
A)4:3
B)15:6
C)45:16
D)15:4
E)27:5
Rationale: Sh:Soaps=8:5
Drinks:Sh=3:4=> 6:8
Drinks:Sh:Soaps= 6:8:5
Soaps:Cer= 9:2=> 9*5:2*5= 45:10
Now, Drinks:Sh:Soaps=> 6*9:8*9:5*9 = 54:72:45
Drinks:Sh:Soaps:cer= 54:72:45:10
Drinks:Cer=54:10=> 27:5 E
Answer: E
Question: What is the remainder if 7^16 is divided by 100?
Options:
A)3
B)4
C)2
D)1
E)5
Rationale: 7^16 can be written as (7^4)^4
If we divide 7^4 by 100 the reminder is 1
So, (7^4)^4 by 100, the reminder is 1^4 = 1
Answer : D
Answer: D
Question: A train crosses a platform of 140 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)887
C)167
D)190
E)161
Rationale: Length of the train be ‘X’
X + 140/15 = X + 250/20
20X +2800 = 15X + 3750
5x=950
X = 190m
Answer: D
Answer: D
Question: The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 10 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 60 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?
Options:
A)250/(30+10A)
B)250/(30+60A)
C)250/50A
D)220/(30+10A)
E)220/40A
Rationale: Since we are dealing with the variables in the answer choices,the best possible method according to me would be substitution.
Substitute A with 3.meaning tommy would have travelled a distance of ((160-10) + (160-60)) in 60 minutes.
250 Kms in 60 minutes ==> 5km/hr.
Substitute A with 3 in the answer options.
Option A
Answer: A
Question: 2 + 2^2 + 2^3 + ... + 2^8 = ?
Options:
A)510
B)610
C)710
D)810
E)910
Rationale: Given series is a G.P. with a = 2, r = 2 and n = 8.
Therefore, sum = a(r^n-1)/(r-1) = 2 x (2^8 –1)/(2-1) = (2 x 255) =510
Answer is A.
Answer: A
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
Options:
A)190
B)180
C)166
D)189
E)191
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: C
Question: How many three-digit integers between 310 and 400, exclusive, are divisible by 3 when the ones digit and the tens digit are switched?
Options:
A)3
B)19
C)22
D)80
E)30
Rationale: Answer is 30
No of digits between 310 and 400 (exclusive) = 400-310-1 = 89
No Intergers divisble by 3 =~ 89/3 ~ 30
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if ones digit and tens digits are switched.
e.g 372 is divisble by 3 (becae 3+7+2= 12 (divisble by 3))
switch digits 732 also divisble by 3 (becae 7+3+2= 12 (divisble by 3))
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if ones digit and tens digits are switched.
You have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1 =30.
Answer : E
Answer: E
Question: A bus leaves Burbank at 8:00 a.m. traveling east at 60 miles per hour. At 2:00 p.m. a plane leaves Burbank traveling east at 300 miles per hour. At what time will the plane overtake the bus?
Options:
A)1:30 p.m.
B)2:50 p.m.
C)3:00 p.m.
D)3:30 p.m.
E)2:25 p.m.
Rationale: At 2:00pm, the bus is 360 miles ahead of plane
The plane travels at 300 mph, which gains 240 mph on bus
360/240=1.5 hours
2:00 + 1:30 = 3:30
The plane will overtake bus at 3:30pm
Answer:D
Answer: D
Question: The value of 5 in the number 357.21 is
Options:
A)5 tenths
B)5 ones
C)5 tens
D)5 hundreds
E)5 twentys
Rationale: Ans: C
The number 357.21 consists of: 3 hundreds, 5 tens, 7 ones, 2 tenths and 1 hundredth =>the value of 5 in 357.21	is 5 tens
Answer: C
Question: Crew A can build a complete car in 20 minutes and Crew B can build a complete car in 25 minutes. If both crews work independently and start at the same time, what is the shortest amount of time W it could take for 10 cars to be complete?
Options:
A)111 1/9 minutes
B)115 2/5 minutes
C)116 minutes
D)120 minutes
E)125 minutes
Rationale: A builds 4 cars in 80 min
B builds 4 cars in 100 min
So A builds another car in another 20 min (i.e total 5 cars)
B builds another car in another 25 minutes (i.e, total 5 cars)
However, A can build another car in next 20 min (i.e total 6 cars)
So total time W= 125 min by B, which is > 120 min by A
B - 4 cars, A - 6 cars
Answer = D
Answer: D
Question: An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?
Options:
A)60°
B)90°
C)180°
D)320°
E)None of these
Rationale: Sol.
Angle traced by the hour hand in 6 hours = [360/12 * 6]° = 180°
Answer C
Answer: C
Question: An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 64 times the difference between the two numbers. How many coins did the old man have?
Options:
A) 24
B) 26
C) 30
D) 64
E) 40
Rationale: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.
x^2 - y^2 = 64(x - y) --> x + y = 64.
Answer: D.
Answer: D
Question: In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Options:
A)5/6
B)3/9
C)5/0
D)5/3
E)5/9
Rationale: Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer: Option A
Answer: A