RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
A.3: 4
B.3: 9
C.3: 2
D.3: 1
Answer: D.3: 1
Explanation: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3: 1
Answer: D
Question: 14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term Z of the sequence?
A.360
B.365
C.369
D.374
Answer: D.374
Explanation: First term , a= 14
Common difference , d = 9
nth term , tn = a + (n-1)d
41st term Z, t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
Question: Evaluate: 45678 * 8*4*8 = ?
A.730848
B.705265
C.730846
D.730596
Answer: A.730848
Explanation: According to order of operations, 8?4?8 (division and multiplication) is done first from left to right
8/4 = 2* 8 = 16
Hence
45678 * 8*4*8 = 45678 * 16 = 730848
correct answer A
Question: Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 15 skiers were CPR certified and 25 were not. How many skiers tried out for the ski patrol?
A.40
B.50
C.60
D.70
Answer: B.50
Explanation: Not Selected = 80%
If total is x.
Then 0.8x=15+25=40
x=50
Hence answer is B.
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
A.Rs.129
B.Rs.198
C.Rs.189
D.Rs.128
Answer: C.Rs.189
Explanation: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100]
= Rs.189.
Answer:C
Question: A part of certain sum of money is invested at 10% per annum and the rest at 16% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
A.8:5
B.4:9
C.4:3
D.4:1
Answer: A.8:5
Explanation: 16:10
= 8:5
Answer: A
Question: The area of the maximum size of the circle described from the 10 inch square?
A.75.5 sq inch
B.76.5 sq inch
C.77.5 sq inch
D.78.5 sq inch
Answer: D.78.5 sq inch
Explanation: 10 inch square means sides of sq are 10inch
then circle is within square so diameter would be 10 inch maximum and radius is 5inch
so area of the circle is = pi*r*r=3.14*5*5=78.5 sq inch
ANSWER:D
Question: What approximate value will come in place of the question mark(?) in the below question?
(47% of 1442 - 36% of 1412) + 63 = ?
A.237
B.278
C.278
D.252
Answer: D.252
Explanation: Explanation:
Since there are 5 cups of each kind,prepared with milk or tea leaves added first,are identical hence,total number of different people ways of presenting the cups to the expert is 10!/(5! x 5!)= 252
Answer: D) 252
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 30 . The largest number is:
A.33
B.77
C.36
D.18
Answer: C.36
Explanation: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 30
15x = 90
x = 6
Largest number = 6x = 36.
ANSWER:C
Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is
A.45 kg
B.75kg
C.25kg
D.35 kg
Answer: A.45 kg
Explanation: Explanation:
Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg.
Answer: A
Question: Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
A.(x + y) / t
B.2(x + t) / xy
C.2xyt / (x + y)
D.2(x + y + t) / xy
Answer: C.2xyt / (x + y)
Explanation: Say the distance to school is 10 miles, x=5 miles per hour and y=1 miles per hour, then:
Time Bob spent biking would be 5/5=1 hour, and time he s pent walking would be 5/1=5 hours, so t=1+5=6 hours.
Now, plug x=5, y=1, and t=6 into the answer choices to see which one yields the distance of 10 miles. Only answer choice C fits.
Answer: C.
Question: Which of the following numbers is between 1⁄4 and 1⁄5?
A..45
B..35
C..29
D..22
Answer: D..22
Explanation: 1/4 = .25
1/5 = .2
The only number between these two is 0.22.
The answer is D.
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
A.16 kmph
B.88 kmph
C.54 kmph
D.18 kmph
Answer: C.54 kmph
Explanation: S = 240/16 * 18/5
= 54 kmph
Answer: C
Question: A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 8.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?
A. 16.5%
B. 9%
C. 35%
D. 55%
Answer: B. 9%
Explanation: The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);
On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.085*fringe benefit costs;
So, 35(S+F) = 30S+85F --> S = 10F --> F/S = 1/10 --> F/(S+F) = 1/(1+10) = 1/11 = 0.09.
Answer: B.
Question: The value of C+5C(7C)(5CC)when C= 7 is:
A.420754
B.420777
C.420170
D.420175
Answer: D.420175
Explanation: Solution:
C+5C(7C)(5CC)
Put the value of C= 7 in the above expression we get,
7+ 35(7 x 7)(5x7 x 7)
= 7+ 35(49)(5 Ã— 49)
= 7 + 420175
=420175
Answer : D
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at?
A.7.42 am
B.7.45 am
C.8.30 am
D.9.45 am
Answer: A.7.42 am
Explanation: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 6 - 1 = 5 rounds per hour.
Time taken to complete one round at this speed = 1/5 hr = 12 min.
ANSWER A
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 apples did each person get before 45 people joined the feast?
A.20.
B.21
C.22
D.23
Answer: C.22
Explanation: if 1430 is divisible by anyone of the answer choices.
A.1430/20 = 143/2
B 1430/21 = 1430/21
C 1430/22 = 65
If 1430 apple was divided among 65 people, each would have received 22.
After addition of 45 people the answer should be 13. 1430/110 = 13.
C is the answer.
Question: In a coded language
If
tomato = 3
apple = 2
math = 1
then
mathematics = ?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: mathematics=4
because no. of vowels in mathematics=4
ANSWER:D
Question: Mike needs 30% to pass. If he scored 212 marks and falls short by 22 marks, what was the maximum marks he could have got?
A.343
B.777
C.780
D.867
Answer: C.780
Explanation: If Mike had scored 22 marks more, he could have scored 30%
Therefore, Mike required 212 + 22 = 234 marks
Let the maximum marks be m.
Then 30 % of m = 234
(30/100) × m = 234
m = (234 × 100)/30
m = 23400/30
m = 780
Answer:C
Question: Latha travels from A to B a distance of 1000 miles in 10 hours. He returns to A in 5 hours. Find his average speed?
A.100mph
B.125.98mph
C.156.15mph
D.133.3mph
Answer: D.133.3mph
Explanation: Speed from A to B = 1000/10 = 100 mph
Speed from B to A = 1000/5 = 200 mph
Average speed = 2*100*200 / 300 = 133.3mph
Answer is D
Question: A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 4 %. The rate of interest obtained is
A.5%
B.5.28%
C.5.30%
D.5.50%
Answer: B.5.28%
Explanation: Shares = 20 shares
50 at 5 discount
rate divident 4%
req ===> 5.28%
ANSWER B
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is
45 kmph. For how many minutes does the bus stop per hour?
A.12
B.11
C.10
D.9
Answer: C.10
Explanation: SPEED OF THE BUS EXCLUDING STOPPAGES = 54 KMPH
SPEED OF THE BUS INCLUDING STOPPAGES = 45 KMPH
LOSS IN SPEED INCLUDING STOPPAGES = 54-45 = 9 KMPH
IN HOUR BUS COVERS 9 KM LESS DUE TO STOPPAGES
HENCE DISTANCE/SPEED = 9/54 = 1/6 HR = 60/6 MIN = 10 MIN
ANSWER C
Question: A rectangular garden is to be twice as long as it is wide. If 180 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?
A.60
B.70
C.80
D.90
Answer: A.60
Explanation: ALTERNATE APPROACH
Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.
Given Perimeter is 180
So, 2 ( L + B ) = 180
Or, L + B = 90
Now use the answer options ( Given Length ; Breath will be half the length)
(A) 60
L = 60 ; B = 30
L + b = 90
(B) 70
L = 70 ; B = 35
L + b = 105
(C) 80
L = 80; B = 40
L + b = 120
(D) 90
L = 90; B = 45
L + b = 135
(E) 100
L = 100; B = 50
L + b = 150
Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (A)
Question: 653Ã—1001=?
A.649011
B.540041
C.654321
D.653001
Answer: D.653001
Explanation: 653Ã—(1000+1)
653000+1
653001
answer D
Question: Three candidates contested an election and received 3834 votes, 7926 votes, and 16240 votes respectively. What percentage of the total votes did the winning candidate receive?
A.55%
B.56%
C.57%
D.58%
Answer: D.58%
Explanation: The total number of votes polled = (3834 + 7926 + 16240) = 28000
The winner's percentage = 16240/28000 * 100 = 58%
The answer is D.
Question: If n = (33)^43 + (43)^32 what is the units digit of n?
A.0
B.2
C.4
D.6
Answer: B.2
Explanation: First of all, the units digit of (33)^43 is the same as that of 3^43 and the units digit of (43)^32 is the same as that of 3^32. So, we need to find the units digit of 3^43 + 3^33.
Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:
3^1=3 (the units digit is 3)
3^2=9 (the units digit is 9)
3^3=27 (the units digit is 7)
3^4=81 (the units digit is 1)
3^5=243 (the units digit is 3 again!)
...
Thus:
The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).
The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (33)^43 + (43)^32 is 7 + 5 = 2.
Answer: B.
Question: If x is a whole number, then x2(x2 - 1) is always divisible by
A.12
B.24
C.12-x
D.multiple of 12
Answer: A.12
Explanation: Sol.
Putting x = 2, we get 22 (22 - 1) = 12.
So, x2(x2 - 1) is always divisible by 12.
Answer A
Question: The average of first 12 even numbers is?
A.10
B.11
C.12
D.13
Answer: D.13
Explanation: Sum of 12 even numbers = 12 * 13 = 156
Average = 156/13 = 13
ANSWER:D
Question: log 3600 is equal to
A.2log6 +1
B.6log2 + 1
C.2log6 +2
D.6log2 + 2
Answer: C.2log6 +2
Explanation: log 3600=log 36 + log 100=2log 6 + 2.
log 36=log 6^2=2log 6
log 100=2.
-->2log 6+2
ANSWER:C
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
A.2828
B.2277
C.2797
D.3900
Answer: D.3900
Explanation: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3
= Rs.3900
D
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?
A.75%
B.67%
C.29%
D.55%
Answer: B.67%
Explanation: 600 --- 400
100 --- ? => 67%
Answer: B
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
A.8
B.10
C.12
D.11
Answer: C.12
Explanation: Speed = 120/10 = 12 m/sec
speed of the second train = 120/5 = 8 m/sec
relative speed = 12+8 = 20 m/sec
Req time = 120+120/20 = 12 sec
ANSWER C
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received Rs.550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs.605 as interest. What was the value of his total savings before investing in these two bonds?
A.Rs.5500
B.Rs.11000
C.Rs.22000
D.Rs.2750
Answer: D.Rs.2750
Explanation: Solution:
Explanatory Answer
Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.
The extra interest earned on the compound interest bond = Rs.55
The interest for the first year =550/2 = Rs.275
Therefore, the rate of interest =55/275 * 100 = 20% p.a.
20% interest means that Shawn received 20% of the amount he invested in the bonds as interest.
If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the bonds = 275/20 * 100 = 1375.
As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = Rs.2750.
Answer D
Question: A train is 360 meter long is running at a speed of 36 km/hour. In what time will it pass a bridge of 140 meter length?
A.11 seconds
B.38 seconds
C.50 seconds
D.88 seconds
Answer: C.50 seconds
Explanation: Speed = 36 Km/hr = 36*(5/18) m/sec = 10 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/10) = 50 seconds
Answer: C
Question: A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 11 members, then what is the exact number of researchers required?
A.33
B.34
C.36
D.31
Answer: D.31
Explanation: 11*3-2( because james is included in all the three teams)
=33-2 =31
D
Question: There are 15 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
A.10
B.30
C.105
D.60
Answer: C.105
Explanation: 15 players are there.
two players play one game with one another.
so 15C2=15x14/2=105
SO OPTION C is correct
Question: Find the odd man out. 10, 20, 30, 40, 50, 60, 72
A.15
B.72
C.51
D.90
Answer: B.72
Explanation: Explanation :
All except 72 are multiples of 10
Answer : Option B
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A.28 km/hr
B.17 km/hr
C.60 km/hr
D.16 km/hr
Answer: C.60 km/hr
Explanation: Let the speed of the slower train be x m/sec.
Then, speed of the train
= 2x m/sec.
Relative speed
= ( x + 2x) = 3x m/sec.
(100 + 100)/8
= 3x => x = 25/3.
So, speed of the faster train = 50/3
= 50/3 * 18/5
= 60 km/hr.
Answer: C
Question: Two vessels contains equal number of mixtures milk and water in the ratio 7:2 and 8:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?
A.1:3
B.9:13
C.5:1
D.11:3
Answer: C.5:1
Explanation: The ratio of milk and water in the new vessel is = (7/9 + 8/9) : (2/9 + 1/9)
= 15/9 : 3/9 = 5:1
Answer is C
Question: Evaluate:434 - 12*3*2 = ?
A.426
B.526
C.626
D.726
Answer: A.426
Explanation: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
434 - 12*3*2 = 434 - 8 = 426
correct answer A
Question: When 15% is lost in grinding wheat, a country can export 30 lakh tons of wheat. On the other hand, if 10% is lost in grinding, it can export 40 lakh tons of wheat. The production of wheat in the country is :
A.20 lakh tons
B.80 lakh tons
C.200 lakh tons
D.800 lakh tons
Answer: C.200 lakh tons
Explanation: Solution
Let the total production be x lakh tons.
Then, 15% of X - 10% of X = (40 - 30) lakh tons
⇔ 5% of x = 10 lakh tons ⇔ x = ( 10x100/5 )= 200 lakh tons.
Answer C
Question: I chose a number and divide it by 4. Then I subtracted 24 from the result and got 10. What was the number I chose?
A.170
B.700
C.800
D.900
Answer: A.170
Explanation: Solution:
Let x be the number I chose, then
x/4âˆ’24=10
x/5=34
x=170
Answer: A
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
A.5/17
B.5/12
C.5/11
D.5/18
Answer: B.5/12
Explanation: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Question: If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/2 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
A.1/4
B.1/2
C.10/3
D.2
Answer: C.10/3
Explanation: N = 2D/5
J = N/2 = D/5
The average of November and January is (N+J)/2 = 3D/5 / 2 = 3D/10
D is 10/3 times the average of November and January.
The answer is C.
Question: A’s speed is 17/15 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
A.1/16
B.2/15
C.2/17
D.1/8
Answer: C.2/17
Explanation: Let x be the fraction of the distance that B runs.
Let v be the speed at which B runs.
The time should be the same for both runners.
Time = D / (17v/15) = xD/v
(15/17)*D/v = x*D/v
x = 15/17
B should have a head start of 2/17 of the full distance.
The answer is C.
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.50 km and 1.0 km respectively. The time taken by the slower train to cross the faster train in seconds is?
A.48
B.9
C.7
D.60
Answer: D.60
Explanation: :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.50 + 1.0 = 2.5 km = 2500 m.
Required time = 2500 * 3/125
= 60 sec.
Answer: D
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
A.2888
B.3120
C.2877
D.2999
Answer: B.3120
Explanation: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Question: A corporation triples its annual bonus to 50 of its employees. What T percent of the employees’ new bonus is the increase?
A.50%
B.662⁄3%
C.100%
D.200%
Answer: B.662⁄3%
Explanation: T of the employees’ new bonus is the increase Hence B.
Question: In order to obtain an income of Rs. 3800 from 70% stock at Rs. 280, one must make an investment of
A.Rs.16000
B.Rs.15000
C.Rs.15250
D.Rs.15200
Answer: D.Rs.15200
Explanation: Explanation :
Market Value = Rs. 280
Required Income = Rs. 3800.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.70 (ie,70% of the face value 100), investment = Rs.280
To obtain Rs.3800, investment = 280/70Ã—3800=Rs.15200
Answer : Option D
Question: the percentage discount offered for"Buy 6 get 1 free is"?
A.14.29%
B.15.29%
C.17.29%
D.19.29%
Answer: A.14.29%
Explanation: Total Items = 7
Discounted = 1
Percentage = 1/7*100
=14.29%
ANSWER:A
Question: The radius of the wheel of a bus is 100 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
A.175
B.250
C.300
D.330
Answer: A.175
Explanation: Radius of the wheel of bus = 100 cm. Then,
circumference of wheel = 2Ï€r = 200Ï€ = 628.57 cm
Distance covered by bus in 1 minute
= 66â„60 Ã— 1000 Ã— 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 440 cm
âˆ´ Revolutions per minute = 6600000/60Ã—628.57 = 175
Answer A
Question: The ratio of boys to girls in a school is 9 to 11. After 36 more girls join, the ratio becomes 9 to 13. How many boys are there in the school?
A.102
B.115
C.132
D.162
Answer: D.162
Explanation: Boys : Girls
9 : 11
let the boys be 9x and the girls be 11x. Now, 36 more girls are added -------> 9:13(new ratio).
so,
9x/(11x+36) =9/13.
solving,
We get : x=18
so No. of boys in the school are :9x= 9*18= 162
hence (D)
Question: In how many ways letters of the word REPEAT be arranged?
A.360
B.120
C.240
D.180
Answer: A.360
Explanation: REPEAT has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 360ways
A
Question: The least number, which when divided by 12, 15, 20 and 63 leaves in each case a remainder of 8 is:
A.448
B.488
C.542
D.1268
Answer: D.1268
Explanation: Required number = (L.C.M. of 12, 15, 20, 63) + 8
= 1260+ 8
= 1268.
answer :D
Question: What will be the cost of building a fence around a square plot with area equal to 25 sq ft, if the price per foot of building the fence is Rs. 58?
A.1160
B.2287
C.2977
D.2668
Answer: A.1160
Explanation: Let the side of the square plot be a ft.
a2 = 25=> a = 5
Length of the fence = Perimeter of the plot = 4a = 20 ft.
Cost of building the fence = 20 * 58 = Rs. 1160.
Answer:A
Question: In a 1000 m race, A beats B by 100 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
A.A)190m
B.B)829m
C.C)822m
D.D)929m
Answer: A.A)190m
Explanation: By the time A covers 1000 m, B covers (1000 - 100) = 900 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/900 * 1000/900 = 1000/810 So, by the time A covers 1000 m, C covers 810 m.
So in 1000 m race A beats C by 1000 - 810 = 190 m.
Answer:A
Question: If 5/w + 5/x = 5/y and wx = y, then the average (arithmetic mean) of w and x is
A.1/2
B.1
C.2
D.4
Answer: A.1/2
Explanation: Given: 5/w + 5/x = 5/ywx=y
Find: (w+x)/2 = ?
5(1/w + 1/x) = 5(1/y) - divide both sides by 5
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A
Question: A car averages 70 mph for the first 4 hours of a trip and averages 60 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip?
A.8
B.9
C.10
D.11
Answer: A.8
Explanation: Let the time for which car averages 60 mph = t
65*(t+4)= 70*4 + 60 t
=>5 t= 20
=> t = 4
Total duration of the trip = 4+4=8
Answer A
Question: If p is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of p?
A.51
B.54
C.162
D.72
Answer: C.162
Explanation: In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.
Answer: C.
Question: In a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 0.8, then the 3rd term is which of the following?
A.−1.5
B.−1
C.0
D.0.2
Answer: D.0.2
Explanation: First = 0.8
Second = 2*0.8-1 = 0.6
Second = 2*0.6-1 = 0.2
Answer: option D
Question: If the side of the regular hexagon above is 2, what is the circumference of the inscribed circle?
A.2∏√3
B.3∏
C.4∏/√3
D.2∏/√3
Answer: A.2∏√3
Explanation: Now AC will be 1 because circle is touching the midpoints of the circle.
Then we get kite ACBO.
We have AC = 1 and CB = 1, now we need to find BO which is radius
from triplets we get 30:60:90 = 1:√3:2
Now CBO is right angled triangle, then we get BO as √3.
r = √3...circumference is 2∏r is 2∏√3.
Answer :option A.
Question: Out of 12 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
A.5/55
B.21/55
C.51/55
D.41/55
Answer: D.41/55
Explanation: P(at least one graduate) = 1 - P(no graduates)
= 1 - 8C₃/12C₃ = 1 - (8 * 7 * 6)/(10 * 11 *12)
= 41/55
Answer: D
Question: If cost of sugar increases by 25%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
A.20
B.10
C.15
D.25
Answer: A.20
Explanation: 100
125
-----
125 ----- 25
100 ------ ? => 20%
ANSWER A