divelab/Sys2Bench huggingface dataset:
Question: All windows are doors. No door is wall
Conclusions:
1. No window is wall
2. No Wall is door
Options:
A)Both 1 and 4 follow
B)Both 1 and 3 follow
C)Both 4 and 1 follow
D)Both 1 and 2 follow
E)Both 1 and 6 follow
Rationale: Explanation:
Since both the premises are universal and one premise is negative, the conclusion must be universal negative. Also, the conclusion should not contain the middle term. So, 1 follows.
However, 2 is the converse of the second premise and thus it also holds.
Answer: D
Answer: D
Question: If 1 + 9 + 11 = 1, Then what is the value of
12 + 11 + 9 = ?
Options:
A)one
B)Ten
C)six
D)five
E)foue
Rationale: Solution:
10
Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1
Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)
Answer B
Answer: B
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
Options:
A)20
B)34
C)37
D)27
E)24
Rationale: There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee
= ⁶C₃ = (6 * 5 * 4)/6
= 20.
Answer: A
Answer: A
Question: There are 3 states and 3 students representing each state. In how many ways can 5 students be chosen such that at Least one student is chosen from each state.
Options:
A)108.
B)118
C)128
D)138
E)148
Rationale: To choose 5 students so that atleast one student will represent each state can be done in two ways:
A. 3-1-1 (3 students from 1 state and 1 student from other two states)
3C1*3C3*3C1*3C1=27
3C1 - # of ways to choose 3-student state;
3C3 - # of ways to choose 3 students from 3-student state;
3C1 - # of ways to choose 1 student from the first 1-student state;
3C1 - # of ways to choose 1 student from the second 1-student state.
OR
B. 1-2-2 (1 student from 1 state and 2 students from other two states)
3C1*3C1*3C2*3C2=81
3C1 - # of ways to choose 1-student state;
3C1 - # of ways to choose 1 student from the 1-student state;
3C2 - # of ways to choose 2 students from the first 2-student state;
3C2 - # of ways to choose 2 students from the second 2-student state.
27+81=108.
Answer: 108 A
Answer: A
Question: 2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges, 2 bananas and 1 apple costs Rs 10. What is the cost of 3 oranges, 3 bananas and 3 apples
Options:
A)22
B)28
C)15
D)77
E)10
Rationale: Explanation:
2 O + 3 B + 4 A = 15 - - - - (1)
3 O + 2 B + 1 A = 10 - - - - (2)
Where A,B and O are number of apple, bananas, and oranges respectively.
Adding 1 and 2,
5 O + 5 B + 5 A = 25 ⇒ 1 O + 1 A + 1 B = 5
now,
3O + 3A + 3B = 5 × 3 = 15
Answer:C
Answer: C
Question: A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent
Options:
A)5400
B)3400
C)5200
D)6500
E)5300
Rationale: Interest for 1 year is the same whether it's simple interest or the compound interest.Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225if 100 is the principal interest =(1225/7350) * 100 = 50/3 %When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %Therefore amount after 2 years = 100 + 325/9 = 1225/9If 1225/9 is the amount principal =100if 7350 is the amount principal =(900/1225)*7350 =5400So sum = 5400; Rate = 50/3 % Answer : A
Answer: A
Question: The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 3:2. As a result of the gift, Kaye had how many more stamps than Alberto?
Options:
A)20
B)30
C)40
D)60
E)80
Rationale: C
K1 = 5x
A1 = 3x
K2 = 5x - 10
A2 = 3x + 10
K2/A2 = 3/2
(5x-10)/(3x+10) = 3/2
2*(5x-10) = 3*(3x+10)
10x - 20 = 9x + 30
x = 50
K2 = 5*50 - 10 = 240
A2 = 3*50 + 10 = 160
K2 - A2 = 80
Answer : E
Answer: E
Question: Two cards are drawn together at random from a pack of 52 cards. What is the probability of both the cards being Queens?
Options:
A)1/221
B)1/712
C)1/224
D)1/212
E)1/232
Rationale: Total number of Queens = 4
Total number of cards = 52
P(Queen in first draw) = 4/52
P(Queen in second draw) = 3/51
=4/52*3/51=1/13*1/17=1/221
Answer A
Answer: A
Question: A printer print a page in 4 second,approx how long time it will take to print 190 page report?
Options:
A)12 Min 40 Sec
B)14 Min 40 Sec
C)16 Min 40 Sec
D)18 Min 40 Sec
E)11 Min 40 Sec
Rationale: 1 Page = 4 Sec
30 Page = 120 Sec (2 Min)
190 Page = 12 Min 40 Sec
ANSWER:A
Answer: A
Question: The prime minister of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the prime minister must sit in the center chair, how many different seating arrangements are possible for the 5 people?
Options:
A) 4
B)24
C) 20
D) 21
E) 120
Rationale: IMO B
Given that one chair is taken, i think the remaining 4 dignitaries can be arranged 4!. That is 4*3*2*1=24.
Answer: B
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
Options:
A)9
B)8
C)7
D)6
E)5
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h = 9 cm
Answer:A
Answer: A
Question: The first three terms of a proportion are 4, 9 and 12. The fourth term is?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: (9*12)/4 = 27
ANSWER:D
Answer: D
Question: The perimeters of 2 squares are 60cm and 48cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
Options:
A)20cm
B)28cm
C)36cm
D)48cm
E)40cm
Rationale: Side of the 1st square = 60/4 = 15cm
Side of the 2nd square = 48/4 = 12cm
Area of the 3rd square = 15^2 - 12^2 = 81cm^2
Side of the 3rd square = 9cm
Required perimeter = 9*4 = 36cm
Answer is C
Answer: C
Question: Compound interest of Rs.4000 at 10% per annum for 1 1/2years will be (interest compounded half yearly).
Options:
A)Rs.473
B)Rs.374
C)Rs.495
D)Rs.630
E)None of the above
Rationale: 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)
So compound interest=4000[1+(5/100)]^3 - 4000=4000[(21/20)^3 -1]
=4000(9261-8000)/8000
=4*1261/8
=630
ANSWER:D
Answer: D
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
If y ≠ 3 and 3t/y is a prime integer greater than 2, which of the following must be true?
I. t = y
II. y = 1
III. t and y are prime integers.
Options:
A) None
B) I only
C) II only
D) III only
E) I and III
Rationale: 3t/y and if t=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.
Answer: A
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 65 liters and they are all empty, how much money total will it cost to fuel all cars?
Options:
A)320$
B)380$
C)420$
D)450$
E)528$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 65 ) = 21 + 507 => 528
Hence answer will be (E) 528
Answer: E
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 50%?
Options:
A)282
B)229
C)356.25
D)285
E)2812
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 50)/100] = Rs. 356.25.
Answer:C
Answer: C
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)7 kmph
C)4 kmph
D)9 kmph
E)2 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2
= 1 kmph
Answer:A
Answer: A
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
Options:
A)1 hour
B)9 hour
C)7 hour
D)6 hour
E)8 hour
Rationale: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è 1 hour
Answer:A
Answer: A
Question: If P * Q implies (P2 + Q2), 8 * (3 * 2) = ?
Options:
A)646
B)86
C)233
D)104
E)640
Rationale: Explanation:
We have, P * Q = (P2 + Q2) ......... Given
8 * (3 * 2) = ?
8 * 13 = (64 +169) = 233
ANSWER C
Answer: C
Question: At the end of the month, a certain ocean desalination plant’s reservoir contained 14 million gallons of water. This amount is twice the normal level. If this amount represents 70% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level?
Options:
A)2
B)5
C)10
D)12
E)15
Rationale: the Q talks of total capacity, normal level, present level, shortage etc..
so it is all about not going wrong in these terms
14 MG= 70% of Total..
total = 14/.7=20MG..
Normal level= 1/2 of 20=10MG..
shortage of normal level=20-10=10MG..
C
Answer: C
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is
Options:
A)0.5928
B)0.5904
C)0.2788
D)0.2699
E)0.2998
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer:B
Answer: B
Question: If a car had increased its average speed for a 210 mile journey by 5 mph, the journey would have been completed in one hour less. What was the original speed of the car for the journey?
Options:
A)40 mph
B)16 mph
C)50 mph
D)20 mph
E)30 mph
Rationale: E
30 mph
Answer: E
Question: Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 66 years. What is Molly's age right now?
Options:
A)15 years
B)35 years
C)25 years
D)45 years
E)55 years
Rationale: Now, Sandy is 66 - 6 = 60
Molly's age is (3/4) * 60 = 45
The answer is D.
Answer: D
Question: list of salaries of 8 employees are listed below. What is the median salary? $40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $32,000
Options:
A)$15,000
B)$23,540
C)$23,550
D)$30,590
E)$31,500
Rationale: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,000, $32,000, $35,500, $40,000, $43,000
Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.
$31,000 + $32,000 = $63,000
The median salary is $31,500.
E
Answer: E
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
Options:
A)XB > YD
B)XB < YD
C)AX > XB
D)AX < XB
E)AX > AB
Rationale: A--X------B
C-----Y---D
XB < YD.
Answer: A.
Answer: A
Question: If a(a + 2) = 80 and b(b + 2) = 80, where a ≠ b, then a + b =
Options:
A)-3
B)-4
C)-6
D)-8
E)-2
Rationale: i.e. if a = 8 then b = -10
or if a = -10 then b = 8
But in each case a+b = -10+8 = -2
Answer:E
Answer: E
Question: A bucket full of worms kept for Mike's next fishing trip was discovered by the rat that resides in the basement. The rat eats a sixth of the total number of worms in 5 hours. How much time will it take the rat to finish a quarter of the worms?
Options:
A)4 hours
B)6 hours
C)7.5 hours
D)8 hours
E)30 hours
Rationale: In 5 hrs, the rat eats 1/6 of the worms.
In 1 hr, it eats (1/6)/5 = 1/30 of the worms. This is his rate of eating.
Worms to be eaten = 1/4. This is the work that has to be done.
Work = Rate * Time
1/4 = 1/30 * Time
Time = 15/2 = 7.5 hrs
Answer (C)
Answer: C
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 41° is?
Options:
A)49m2
B)50m2
C)51.5m2
D)53m2
E)59m2
Rationale: 41/360 * 22/7 * 12 * 12
= 51.5 m2
Answer:C
Answer: C
Question: A man can row upstream at 25 kmph and downstream at 43 kmph, and then find the speed of the man in still water?
Options:
A)86
B)34
C)30
D)15
E)17
Rationale: US = 25
DS = 43
M = (43 + 25)/2
= 34
Answer: B
Answer: B
Question: If logx 4 = 1/4, then x is equal to
Options:
A)16
B)64
C)128
D)256
E)none
Rationale: Solution
log x 4	= 1/4
‹=› x 1/4
= 4
‹=›x= 44
= 256.
Answer D
Answer: D
Question: A shop owner sells 90 oranges and gains SP of 20 oranges. Find the gain %?
Options:
A)25 4/7%
B)27 4/7%
C)30 4/7%
D)29 4/7%
E)28 4/7%
Rationale: Gain=20 orangesTotal 90 orangesCP 90-20=70(20/70)*100=28 4/7%Ans E
Answer: E
Question: Siva Reddy walked 2 km west of his house and then turned south covering 4 km. Finally, He moved 3 km towards east and then again 1 km west. How far is he from his initial position?
Options:
A)10 km
B)9 km
C)2 km
D)4 km
E)8 km
Rationale: 4 km
ANSWER D
Answer: D
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.6400?
Options:
A)8100
B)3388
C)7767
D)2009
E)22888
Rationale: 6400* 9/8 * 9/8
= 8100
Answer: A
Answer: A
Question: A Jar contains a mixture of AB in the ratio 4:1. When 40 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.
Options:
A)12
B)15
C)16
D)64
E)25
Rationale: 40 litres of mixture that is replaced will contain 32 litres of A and 8 litres of B (as A:B = 4:1)
Let the initial volume of the mixture be 4K + 1K = 5K
So by condition ,
[ 4K-32 ]/ [ K-8+40 ] = 2/3 => 12K -96= 2K-16+80 => 10K = 160
Solve for K which is K = 16
So initial volume of liquid A = 4K = 64 litres
Answer : D
Answer: D
Question: The average of 11 numbers is 10.8. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
Options:
A)9.5
B)12.6
C)10.5
D)11.5
E)12
Rationale: Explanation:
1 to 11 = 11 * 10.8 = 118.8
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 118.8 = 12.6
6th number = 12.6
Option B
Answer: B
Question: John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
Options:
A)40 m
B)50 m
C)70 m
D)90 m
E)100 m
Rationale: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2 =310
By rule of alligation,
concentration of water in mixture1 (29)
concentration of water in pure water (1)
Mean concentration
(310)
1−310=710
310−29=790
=> Quantity of mixture1 : Quantity of water
=710:790=110:190=1:19
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water =1:19
=> Quantity of water =630×19=70 ml
C
Answer: C
Question: The inverse ratio of 3: 6: 1 is?
Options:
A)2:3:7
B)2:3:9
C)2:1:6
D)2:3:6
E)2:3:1
Rationale: 1/3: 1/6: 1/1 = 2:1:6
Answer:C
Answer: C
Question: Two girls begin together to write out a book containing 900 lines. The first girl starts with the first line, writing at a speed of 150 lines per hour and the second girl starts writing from the last line at the rate of 200 lines per hour. At which line will they meet?
Options:
A)384th line
B)386th line
C)389th line
D)400th line
E)None of these
Rationale: Explanation :
Solve this question as analogous to distance method,
At some x page they will meet, so
x/150 = (900 – x)/200, we get x = 385.7 = 386th line (approx.)
Answer –B
Answer: B
Question: A man can do a job in 5 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
Options:
A)6.3
B)6.9
C)3.5
D)6.1
E)6.2
Rationale: 1 day work of the three persons = (1/5 + 1/20 + 1/25) = 29/100
So, all three together will complete the work in 100/29 = 3.5 days.
Answer:C
Answer: C
Question: A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 30 paise per sq m is
Options:
A)Rs. 223.20
B)Rs. 323.20
C)Rs. 423.20
D)Rs. 523.20
E)None of these
Rationale: Explanation:
Area to be plastered = [2(l + b) Ã— h] + (l Ã— b)
= [2(25 + 12) Ã— 6] + (25 Ã— 12) = 744 sq m
Cost of plastering = 744 Ã— (30/100) = Rs.223.20 Answer: A
Answer: A
Question: A basket contains 2 blue, 2 red and 2 yellow marbles. If 2 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
Options:
A)2/5
B)3/25
C)1/6
D)9/28
E)11/24
Rationale: 6/6*4/5*2/4 = 2/5
the answer is (A)
Answer: A
Question: The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paise per meter is Rs. 36. The breadth of the room is ?
Options:
A)6 meters
B)7 meters
C)8 meters
D)9 meters
E)10 meters
Rationale: Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m2
= 90 m2
∴ Area of the room = 90 m2
Breadth of the room = Area /Length
= 90 / 15 m
= 6m
Answer : A
Answer: A
Question: A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.
Options:
A)10 sec
B)12 sec
C)14 sec
D)16 sec
E)20 sec
Rationale: ANSWER B
As we need to get answer in seconds, so never forget to convert speed into meter per second.
Speed = 30 km/hr = 30* 5/18 m/sec
= 25/3 m/sec
Distance = length of train = 100 meter
Required time = DIST/SPEED = 100/25/3 = 100*3/25 = 12sec
ANSWER B
Answer: B
Question: Population of a city in 20004 was 1200000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
Options:
A)354354
B)545454
C)465785
D)456573
E)1300650
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1300650
E
Answer: E
Question: Gary’s Gas Station serves an average of 14 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?
Options:
A)1,104
B)1,200
C)1,240
D)1,280
E)1,320
Rationale: 6 a.m. to 10 p.m. = 16 hours
Number of cars serviced on weekdays = (16 * 9 * 5)
Number of cars serviced on Saturday = (16 * 14)
Number of cars serviced on Sunday = (16 * 10)
Number of cars served in a week = 16(45 + 14 + 10) = 16 * 69 = 1104
Answer: A
Answer: A
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
Options:
A)4 days
B)7 days
C)9 days
D)8 days
E)2 days
Rationale: C
3/12 + (3 + x)/16 = 1
x = 9 days
Answer: C
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently seven spaces behind player B, what is the probability that player B will be frozen after player A rolls?
Options:
A)1/12
B)5/36
C)1/6
D)1/3
E)17/36
Rationale: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 7 (as A is 7 spaces behind B) = 6 ( (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) )
So, the probability = 6/36 =1/6 (Option C)
Answer: C
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)999
C)8289
D)2889
E)2132
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A
Answer: A
Question: n^(n/2)=6 is true when n=6 in the same way what is the value of n if n^(n/2) =10?
Options:
A)8
B)12
C)10
D)16
E)18
Rationale: n^(n/2)=10Apply logN/2logn=log10nlogn=2log10=log10^2=log100Logn=log100Now apply antilogn=100/nNow n=10.ANSWER:C
Answer: C
Question: If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, which of the following MUST be true?
I. xy(z + 1) is even.
II. x(z + y) is even.
III. (x^2 - x)yz is even.
Options:
A)I only
B)III only
C)I and II
D)II and III
E)I, II, and III
Rationale: If x is even, then the average of even number of odd consecutive integers (y), will be even. For example, the average of {1, 3} is 2.
If x is odd, then the average of odd number of odd consecutive integers (y), will be odd. For example, the average of {1, 3, 5} is 3.
Thus:
If x = even, then y = even;
If x = odd, then y = odd.
Next, |z - 6/4| = 1/2:
z - 6/4 = 1/2 --> z = 2;
-(z - 6/4) = 1/2 --> z = 1.
Since, z can be even as well as odd, then it takes no part in deciding whether the options are even or odd. So, we can ignore it.
I. xy(z + 1) is even: xy can be odd if both are odd and even if both are even. So, this option is not necessarily even. Discard.
II. x(z + y) is even: if x and y are odd, and z is even, then x(z + y) = odd(odd + even) = odd but if if x and y are odd, and z is odd too, then x(z + y) = odd(odd + odd) = even. So, this option is not necessarily even. Discard.
III. (x^2 - x)yz is even: (x^2 - x)yz = x(x - 1)yz. Since either x or x - 1 is even, then the whole expression must be even irrespective of the values of x, y, and z.
Answer: B.
Answer: B
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
Options:
A)Rs.45
B)Rs.78
C)Rs.44
D)Rs.40
E)Rs.42
Rationale: Explanation:
Ï€ (152 - 132) = 176
176 * 1/4 = Rs.44
ANSWER IS C
Answer: C
Question: 3 OUT OF 1000 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
Options:
A)11/50
B)2/9
C)1/45
D)2/7
E)NONE OF THESE
Rationale: REQUIRED PERCENTAGE=(3/1000*100)%=2/7%
CORRECT OPTIONS: D
Answer: D
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
Options:
A)7189
B)7282
C)7298
D)1500
E)1576
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
Answer: D
Answer: D
Question: The parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 16 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
Options:
A)28.28CM
B)25.45CM
C)26.45CM
D)20.18CM
E)32.14CM
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(20 + 16) = 72 cm Parameter of the square = 72 cm
i.e. 4a = 72
A = 18
Diameter of the semicircle = 18 cm
Circimference of the semicircle
= 1/2(∏)(18)
= 1/2(22/7)(18) = 396/14 = 28.28 cm to two decimal places
Answer: A
Answer: A
Question: The ratio of red, yellow, and green jelly beans in a jar is 2:3:4. If the number of jelly beans is increased by 50%, 40%, and 30% respectively, what will be the new ratio?
Options:
A)7:15:21
B)11:18:24
C)15:21:26
D)17:24:28
E)18:25:32
Rationale: The new ratio will be 3:4.2:5.2=30:42:52=15:21:26.
The answer is C.
Answer: C
Question: If x is an integer, then x(x - 1)(x - k) should be evenly divisible by three when k is any of the following values EXCEPT
Options:
A)4
B)-4
C)-1
D)2
E)5
Rationale: if we put k=-1 we get:
X(x-1)(X+1) rearrange:(x-1)X(X+1)
so it looks like a sequenc,
if we assume that X =2 and put number from the answer then we get:
(x – 1)x(x – k)
k=5 =1.2.-3
k=2 =1.2.0
k=-1 =1.2.3
k=-4 =1.2.6
but when we put
k=4 =1.2.-2 not satisfied
so,the answer is A
Answer: A
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,560 ?
Options:
A)$12
B)$14
C)$24
D)$17
E)$18
Rationale: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,560, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,560 --> (5+x)(20-x)=156 --> x=7 or x=8 --> price=10+$2*7=$24 or price=10+$2*8=$26.
Answer: C.
Answer: C