divelab/Sys2Bench huggingface dataset:
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
Options:
A)228
B)299
C)266
D)500
E)188
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500
Answer:D
Answer: D
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
Options:
A)230
B)387
C)277
D)299
E)213
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.Answer:A
Answer: A
Question: (51+ 52 + 53 + ... + 100) = ?
Options:
A)2775
B)2785
C)2975
D)3775
E)4000
Rationale: This is an A.P. in which a = 51, l = 100 and n = 50.
Sum =	n	(a + l)	=	50	x (51 + 100) = (25 x 151) = 3775.
2	2
D)
Answer: D
Question: A right triangle has sides of a, b, and 15, respectively, where a and b are both integers. What is the value of (a + b)?
Options:
A)220
B)221
C)225
D)224
E)226
Rationale: LET a= hypotenuse , b =base ,15 = perpendicular . therefore a^2 -b^2 =15^2 or (a+b)(a-b) = 225
a+b =225/a-b ' a-b cannot be zero ..therefore a+ b =225 where a-b is equal to 1
C
Answer: C
Question: Find the area of circle whose radius is 8.2m?
Options:
A)138
B)154
C)288
D)211.3
E)371
Rationale: 22/7 * 8.2 * 8.2
= 211.3
Answer:D
Answer: D
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9 sec
B)13.8 sec
C)53.8 sec
D)10.8 sec
E)10.4 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer: D:
Answer: D
Question: 5358 x 51 = ?
Options:
A)273762
B)283758
C)273298
D)273258
E)277382
Rationale: D
273258
5358 x 51 = 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
Answer: D
Question: 30 men take 20 days to complete a job working 9 hours a day. how many hour a day should 40 men work to complete the job?
Options:
A)6.79
B)6.75
C)6.71
D)6.74
E)6.712
Rationale: Explanation:
Let the capacity of man in hour is 1 unit. Then total work = 30 × 20 × 9
40 men in 20 days working t hours a day can complete = 40 × 20 × t
⇒ 40 × 20 × t = 30 × 20 × 9
⇒ t = 6.75 hours.
Answer: B
Answer: B
Question: A computer can perform c calculations in s seconds. How many minutes will it take the computer to perform A calculations?
Options:
A)60as/c
B)as/c
C)as/60c
D)60c/as
E)a/60cs
Rationale: As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES.
We're told that a computer can perform a calculations in S seconds.
Let's TEST....
a = 2
S = 3
2 calculations every 3 seconds =
40 calculations every 1 minute
We're asked how many MINUTES it will take to perform K calculations.
Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST...
K = 80
So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80
Answer A: 60KS/a = 60(80)(3)/2 = 7200 This is NOT a match
Answer B: KS/a = (80)(3)/2 = 120 This is NOT a match
Answer C: KS/60a = (80)(3)/(60)(2) = 2 This IS a match
Answer D: 60a/KS = 60(2)/(80)(3) = 1/2 This is NOT a match
Answer E: K/60aS = 80/(60)(2)(3) = a fraction. This is NOT a match
C
Answer: C
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A ?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Explanation:
(A+B) - (B-C) = 12 <=> A - C = 12. Answer: A
Answer: A
Question: How many possible integer values are there for x if |2x - 3| < 6 ?
Options:
A)One
B)Two
C)Three
D)Four
E)Six
Rationale: Solution: |2x-3| < 6
let 2x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =2x ==> -3<2x<9
dividing all values by +4 we have -1.5 <x < 4.5
Now question says Integer values (not rational ) therefore we have -1,0,1,2, 3, 4
Hence 6 E
Answer: E
Question: It is currently 7:05 PM. What time was it in the morning exactly 51,132 minutes ago?
Options:
A)6:53
B)6:55
C)6:59
D)7:03
E)7:09
Rationale: Convert 51,132 minutes to hours by dividing by 60: 51,132/60 = 852 R12. That is 852 hours, 12 minutes. Convert 852 hours to days by dividing by 24: 852/24 = 35 R12. That is 35 days, 12 hours. Thus 852 hours before 7:05 PM is 12 hours before 7:05 PM which is 7:05 AM. 12 minutes before that is 6:53 AM. A
Answer: A
Question: Of the 400 math majors at a certain university, 30 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) 80
Rationale: 30% of students are assigned to Monday and Wednesday = 0.3*400 = 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 E.
Answer: E
Question: If a is a positive integer then 1^(2a) + (1^a)/(1^(2a)) =
Options:
A)3
B)4
C)2
D)5
E)6
Rationale: 1^(2a) + 1^a/ 1^(2a) = 1^a + 1^a/1^a = 1+ 1 =2
Answer : C
Answer: C
Question: A batsman makes a score of 90 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
Options:
A)25
B)31
C)27
D)29
E)42
Rationale: Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 90 = Total runs scored in 17 innings
=> 16(x-3) + 90 = 17x
=> 16x - 48 + 90 = 17x
=> x = 42
Answer is E.
Answer: E
Question: If the product of two positive integers is 120, which of the following could be the LCM and HCF of the two numbers? a. LCM 60 : HCF 2 b. LCM 30 : HCF 4 c. LCM 12 : HCF 10
Options:
A)b only
B)c only
C)b,c only
D)a only
E)a,c only
Rationale: The right answer is a.
Answer : D
Answer: D
Question: What is the lowest positive integer that is divisible by 1 through 2, inclusive?
Options:
A)2
B)4
C)8
D)6
E)1
Rationale: The integer should be divisible by: 1 and 2. The least common multiple of these integers is LCM=1*2=2
Answer: A
Answer: A
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Options:
A)33 1/8%
B)33 7/3%
C)33 1/3%
D)37 1/3%
E)32 1/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: C
Question: In how many ways Chief Minister and Minister be elected from a team of 13 members?
Options:
A)128
B)131
C)132
D)143
E)156
Rationale: To do this, if captain is elected first, then we have 13 ways of doing this.
For election of vice-captain, we have only 12 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 13*12 = 156 ways.
Answer : E
Answer: E
Question: Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits allowed)
Options:
A)801
B)106
C)216
D)108
E)116
Rationale: There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 6 ways each. Required number of numbers =3x6x6=108. Ans: D
Answer: D
Question: The side of a rhombus is 20 m and length of one of its diagonals is 16 m. The area of the rhombus is?
Options:
A)223.28
B)293.28
C)293.78
D)291.28
E)193.28
Rationale: area of the rhombus = 1/2 * p * √4(a)2 - (p)2
a= 20 ; p = 16
A=1/2 * 16 *√4(20)2 - (16)2
=1/2 * 16 *√1600 - 256
=1/2 * 16 *√1344
A =293.28
Answer : B
Answer: B
Question: A certain high school has 500 students. Of these students, 20 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
Options:
A)430
B)440
C)450
D)460
E)470
Rationale: We're given a series of facts to work with:
1) A certain high school has 500 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.
We're asked how many students are taking NEITHER music nor art?
Let's TEST
X = 20
Y = 20
Z = 10
So, we have 20 students taking music, 20 taking art and 10 taking BOTH music and art. That 10 person has been counted TWICE though (once in the music 'group' and once in the art 'group'), so what we really have is...
10 student taking JUST music
10 student taking JUST art
10 student taking BOTH music and art
Total = 30 students
We're asked for the total number of students who are taking NEITHER Course. That is 5000 - 30 = 470.
E
Answer: E
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?
Options:
A)Rs.43000
B)Rs.50000
C)Rs.57000
D)Rs.60000
E)Rs.62000
Rationale: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 60 * 950
= Rs.57000
C
Answer: C
Question: In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,7). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
Options:
A)4/7
B)2/3
C)3/5
D)3/7
E)1/2
Rationale: The area of the right triangle is (1/2)*4*7 = 14.
Only the points (a,b) below the line y=x satisfy a - b > 0.
The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.
P(a - b > 0) = 8/14 = 4/7
The answer is A.
Answer: A
Question: Given a spinner with four sections of equal size labeled A, B, C, and D, what is the probability of NOT getting an A after spinning the spinner two times?
Options:
A)15/16
B)9/16
C)1/2
D)1/4
E)1/8
Rationale: The probability of NOT getting an A after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Answer: B
Question: The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
Options:
A)60
B)70
C)50
D)20
E)cannot be determined
Rationale: Let the ten's digit be x and unit's digit by y
Then, x + y = 15 and x - y = 3 or y - x = 3
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9
So, the number is either 96 or 69.
Hence, the number cannot be determined.
ANSWER E
Answer: E
Question: A collection of books went on sale, and 2/3 of them were sold for $2.00 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?
Options:
A)$144
B)$135
C)$90
D)$60
E)$54
Rationale: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($2.00) or $144. The best answer is therefore A.
Answer: A.
Answer: A
Question: A certain fraction has the same ratio to 1/18, as 2/5 does to 2/9. What is this certain fraction?
Options:
A)1/5
B)1/7
C)1/10
D)1/12
E)1/15
Rationale: x / (1/18) = (2/5) / (2/9)
x = 2*9*1 / 18*5*2 = 1/10
The answer is C.
Answer: C
Question: The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker’s discount and the banker’s gain.
Options:
A)120
B)121
C)130
D)151
E)None
Rationale: Sol.
T.D. = √P.W. * B.G.
∴ B.G. = (T.D.)² / T.W. = Rs. [110 * 110 / 1100] = Rs. 11.
∴ B.D. = (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.
Answer B
Answer: B
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
Options:
A)197
B)127
C)189
D)400
E)198
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: D
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is :
Options:
A)123
B)127
C)235
D)305
E)None of these
Rationale: Solution
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127. Answer B
Answer: B
Question: The average of 11 numbers is 10.4. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
Options:
A)9
B)9.2
C)10
D)11.5
E)17
Rationale: Explanation:
1 to 11 = 11 * 10.4 = 114.4
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 114.4 = 17
6th number = 17
E
Answer: E
Question: The surface area of a cube is 486 Cm3. Find its volume
Options:
A)729
B)739
C)759
D)749
E)719
Rationale: Let each edge of the cube be a Cm.
Then 6 a(power)2 = 486 => a(power)2 = 81 = 9(power)2 => a = 9
Volume = a(power)3 = 9(power)3 Cm(power)3 => 729 Cm(power)3
Answer is A.
Answer: A
Question: Including Cara and Dan, there are six members on the board of directors for a company. If the board is to be split up into a four-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?
Options:
A)3/5
B)4/5
C)3/10
D)7/10
E)11/20
Rationale: The number of possible subcommittees with Cara is 5C3=10.
The number of possible subcommittees with Cara and Dan is 4C2=6.
The fraction of Cara's subcommittees which include Dan is 6/10=3/5.
The answer is A.
Answer: A
Question: Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
Options:
A)2:7
B)2:3
C)2:0
D)2:1
E)2:2
Rationale: Explanation:
By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
{\color{Blue} \therefore } Required ratio = 60 : 90 = 2 : 3
Answer: B) 2:3
Answer: B
Question: A man in a train travelling at 25km/hr notices that a train going in the opposite direction passes him in 10 sec.If the length of this train is 110m find its speed .
Options:
A)30 km/hr
B)40 km/hr
C)50 km/hr
D)60 km/hr
E)70 km/hr
Rationale: relative speed of trains = 110/10 mtrs/sec = 110*18/(10*5)= 40 km/hr
speed of 2nd train = 110-40=70 km/hr
ANSWER:E
Answer: E
Question: A girl goes to her office for work which is 50 miles. She goes to her office few distance by bicycle and remaining by train. The speed of bicycle is 15 mph and that of train is twice of bicycle. If she spend 20 min. more on bicycle, then total time taken by her from going to office from her home?
Options:
A)1 hr 20 min
B)2 hr 20 min
C)2 hr 30 min
D)2 hr 40 min
E)2 hr 50 min
Rationale: Let time travelled in train is x min then in cycle (x+20) min.
(30/60)x + (15/60)(x + 20) = 50 or x = 60
Total time taken 60 + (60 + 20) = 2 hr 20 min
ANSWER:B
Answer: B
Question: A man can row upstream at 8km/hr and down stream at 11km/hr find mans rate in still water ?
Options:
A)9.5km/hr
B)4.5km/hr
C)6.5km/hr
D)3.5km/hr
E)5.5km/hr
Rationale: :	given upstream(u) =8km/hr
down stream (v)= 11km/hr rate in still water =1/2(u+v)=1/2(8+11)=9.5km/hr Answer is (A):9.5
Answer: A
Question: There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that atleast two blue socks have been chosen?
Options:
A)23
B)37
C)97
D)20
E)21
Rationale: Explanation:
Number of red socks = 30 × 60% = 18
If you draw out 18 socks there's a possibility that all of them are red
If you draw out 19 socks one of them has to be a blue one
And if u draw 20 socks then definitely 2 of them are blue socks
So the answer is 20.
Answer:D
Answer: D
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease?
Options:
A)90%
B)30%
C)40%
D)70%
E)80%
Rationale: The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)*100 = (0.9)*100 = 90%.
A
Answer: A
Question: Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 16 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
Options:
A) 6
B) 9
C) 10
D) 12
E) 15
Rationale: This is an inverse proportional problem......
5 pipes in 16 days; So for 4 days, it will be = 16 x 5 / 4 = 20
So, 20-5 = 15
Answer E
Answer: E
Question: If two drawers of socks contains five different colored socks in each drawer, and a sock is randomly selected from each drawer, what is the probability of getting a pair of the same colored socks?
Options:
A)2/5
B)1/5
C)1/6
D)1/2
E)4/5
Rationale: A pair of matching socks.
First solve for NO matching socks:
1st drawer = any color = 5/5
2nd drawer = not a match to the first = 4/5
(5/5)(4/5) =
(1)(4/5) =
20/25
4/5 is the probability of NO matching socks, so...
1 - 4/5 = 1/5 = the probability of getting at least one matching pair of socks.
Answer: B
Answer: B
Question: what is the angle between the hands of a clock when time is 8:20?
Options:
A)65deg
B)75deg
C)50deg
D)15deg
E)30deg
Rationale: Angle between two hands =
20h - 11/2 m = 20*8 - 20*11/2 = 160 - 110 = 50deg
ANSWER:C
Answer: C
Question: The lettersmove four steps backward to obtain the letters of the next term
?, SIY, OEU, KAQ, GWM, CSI
Options:
A)AAH
B)AHU
C)WMC
D)RTR
E)UGV
Rationale: C
WMC
The lettersmove four steps backward to obtain the letters of the next term
Answer: C
Question: Priya covers journey from kavali to nellore by car at average speed of 70 Km/hr. She returns back by scooty with an average speed of 70 Km/hr. Find her average speed during the whole journey?
Options:
A)60Km/hr
B)70Km/hr
C)80Km/hr
D)90Km/hr
E)100km/hr
Rationale: Explanation:
Average speed = 2 xy/x+y
= 2*70*70/140
= 70 Km/hr
Answer: Option B
Answer: B
Question: Of the 200 people attending a conference, 60 have signed up for the Marketing workshop and 180 have signed up for the Accounting workshop. If 50 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:
Options:
A)60
B)75
C)80
D)85
E)90
Rationale: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:
Total = Gp.1 + Gp.2 - Both + Neither
200 = 60 + 180 - Both + 50
200 = 290 - Both
Both = 90
Final Answer:
E
Answer: E
Question: Lebron has 297 bottles of beer in his fridge and is inviting eight friends over to drink and watch the game. He wants to make things seem as if everybody will get the same amount of beer. How many beers will he have to drink in order maintain the illusion that he is sharing equally amongst his friends?
Options:
A)1
B)4
C)2
D)8
E)0
Rationale: Using the divisibility rule of nine, we add the digits of 297 together and get the number 18. 18 is divisible by 9 and our answer is 0 beers(option E)
Answer: E
Question: By selling an umbrella for Rs. 300, a shop keeper gains 15%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
Options:
A)6.5%
B)2%
C)5.88%
D)3%
E)4%
Rationale: Marked price = Rs. 300
C.P. = 100/115 * 300 = Rs. 255
Sale price = 90% of Rs. 300 = Rs. 270
Required gain % = 15/255 * 100 =5.88%.
Answer: C
Answer: C
Question: 3 candidates in an election & received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidategot in that election?
Options:
A)50%
B)52%
C)57%
D)60%
E)65%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: C
Question: Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
Options:
A)72 sec
B)132 sec
C)192 sec
D)252 sec
E)None
Rationale: Solution
Relative Speed	= (45 - 40 ) Kmph
= 5 kmph
=(5 x 5 / 18)m/sec
= (25 / 18 ) m/sec
Time taken	= (350 x 18 / 25) sec
= 252 sec.
Answer D
Answer: D
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
Options:
A)8
B)7
C)4
D)3
E)2
Rationale: 150 = (750*5*R)/100
R = 4%
Answer: C
Answer: C
Question: 10 men, working 3 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
Options:
A)3 hours a day
B)5 hours a day
C)6 hours a day
D)7 hours a day
E)8 hours a day
Rationale: Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[men 15 10
days 12 18] ::3:x
=>xâˆ—15âˆ—12=10âˆ—18âˆ—3
=>x=10âˆ—18âˆ—3/ 15âˆ—12
=>x=3
Option A
Answer: A
Question: Find the smallest number of four digits exactly divisible by 4,5,7 and 8.
Options:
A)1150
B)1160
C)1140
D)1152
E)1145
Rationale: Smallest number of four digits is 1000.
Required number must be divisible by L.C.M. of 4,5,7,8 i.e 280,
On dividing 1000 by 280,we get 120 as remainder.
Therefore, Required number = 1000 +( 280 â€“ 120 ) = 1160.
Answer is B.
Answer: B
Question: Two persons start at the same point, walk in opposite directions with 6 km/hr and 7 km/hr respectively.
What is the distance separated after 3 and half hrs?
Options:
A)45.5 km
B)27.250 km
C)28.250 km
D)29.250 km
E)25.250 km
Rationale: As the two persons are moving in the opposite direction, so they will be separateed in 1 hour = 6 + 7 = 13 km.
They will be separated in 2.5 hours = 13 * 3.5 = 45.5 km
ANSWER:A
Answer: A
Question: 3889 + 12.952 – ? = 3854.002
Options:
A)47.095
B)47.752
C)47.932
D)47.95
E)None
Rationale: EXPLANATION
Let 3889 + 12.952 – x = 3854.002.
Then x = (3889 + 12.952) – 3854.002
= 3901.952 – 3854.002
= 47.95.
Answer D
Answer: D
Question: Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
Options:
A)2/5525
B)3/5525
C)2/5525
D)2/5526
E)4/5525
Rationale: Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
A)
Answer: A
Question: An woman swims downstream 45 km and upstream 25 km taking 5 hours each time; what is the speed of the current?
Options:
A)2
B)1
C)3
D)4
E)2.1
Rationale: 45 --- 5 DS = 9
? ---- 1
25---- 5 US = 5
? ---- 1 S = ?
S = (9 - 5)/2 = 2
Answer: A
Answer: A