mathewhe/aqua_rat huggingface dataset:
Question: How many times does the minute hand go round in a day?
(A) 21
(B) 20
(C) 12
(D) 26
(E) 25
Rationale: C
12
period = 65 minutes/60 minutes = 1.08.
The number of cycles per hour then = 1/period = 1/1.08 = .923.
The number of cycles in 24 hours, then = (0.923)(24) = 22.153. That's how you compute how many times the minute hand catches up the hour hand in 24 hours (round to 22)
Answer: (C) 12
Question: If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.
(A) $ 40.
(B) $ 50.
(C) $ 60.
(D) $ 70.
(E) None
Rationale: Solution:
Cost of 20 lollipops = $90
Sold each lollipop for $2
So he sold 20 lollipops for $(20 × 2) = $40
Loss = $(90 – 40) = $50
Therefore, loss = $ 50.
Answer B
Answer: (B) $ 50.
Question: A committee has 3 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 127
(B) 60
(C) 882
(D) 272
(E) 323
Rationale: The number of ways to select two men and three women
= 3C₂ * ⁶C₃
= (3 *2 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 60
Answer: B
Answer: (B) 60
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $12. If the shop keeper has a order of 200 articles, how much profit he will get?
(A) 200
(B) 2000
(C) 1500
(D) 400
(E) 600
Rationale: Total money after selling articles = 200*12 = 2400
cost price = 200*10 = 2000
profit = 400
correct option is D
Answer: (D) 400
Question: Last year, the price of a vacation package was P. At the beginning of this year, the price went up 45%. Lucas used a travel voucher to purchase the vacation package at 35% off this year’s price. In terms of P, how much did Lucas pay?
(A)  P + 10
(B)  0.91*P
(C)  0.92*P
(D)  0.93*P
(E)  0.94*P
Rationale: Last year price = P;
This year price = 1.45P;
Lucas used a travel voucher to purchase the vacation package at30%offthis year’s price, thus he paid (1 - 0.35)*1.45P = 0.94P.
Answer: E.
Answer: (E)  0.94*P
Question: For all even integers n, h(n) is defined to be the sum of the even integers between 6 and n, inclusive. What is the value of h(18)/h(10) ?
(A)  1.8
(B)  4
(C)  6
(D)  18
(E)  60
Rationale: CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then
Mean = Median =(First+Last)/2
and Sum = Mean*Number of terms
h(18) = [(6+18)/2]*7 = 84
h(10) = (6+10)/2]*3 = 24
h(18)/h(10) = (84) / (24) ~ 4
Answer : B
Answer: (B)  4
Question: A certain article of clothing was discounted during a special sale to 4/5 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?
(A) 50%
(B) 33.33%
(C) 40%
(D) 16.66%
(E) 12.5%
Rationale: Say the original retail price of the item was $200.
The price after the first sale = 4/5 * $200 = $160.
The price after the second sale = 1/2 * $200 = $100.
The percent change from the first sale to the second = (160 - 100) / 150 = 1/3 = 40%.
Answer: C.
Answer: (C) 40%
Question: Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) s.10
(B) s.2
(C) s.5
(D) s.3
(E) s.4
Rationale: 2500 = D(100/4)2
D = 4
ANSWER:E
Answer: (E) s.4
Question: The height of the wall is 6 times its width and length of the wall is 7 times its height .if the volume of the wall be 86436 cu.m.its width is
(A) 4m
(B) 5m
(C) 6m
(D) 7m
(E) 8m
Rationale: Explanation:
Let width = x
Then, height=6x and length=42x
42x Ã— 6x Ã— x = 86436
x = 7
Answer: D
Answer: (D) 7m
Question: If m = 3^n, what is the greatest value of n for which m is a factor of 31!
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Solution-
Consider multiples of 25!=> 3,6,9,12,15,18,21,24,27,30
Count no. of 3 in each multiple.
3=3x1->1
6=3x2->1
9=3x3->2
12=3x4->1
15=3x5->1
18=3x3x2->2
21=3x7->1
24=3x8->1
27=3x3x3->3
30=3x10->1
---- count 3's =14 so answer is 14
Answer : D
Answer: (D) 14
Question: A watch was sold at a loss of 12%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 875
(B) 2876
(C) 1977
(D) 2778
(E) 2711
Rationale: 88%
104%
--------
16% ---- 140
100% ---- ? => Rs.875
Answer: A
Answer: (A) 875
Question: A single discount equivalent to the discount series of 30%, 20% and 10% is?
(A) 31.8
(B) 31.1
(C) 31.6
(D) 31.2
(E) 49.6
Rationale: Explanation:
100*(70/100)*(80/100)*(90/100) = 50.4
100 - 50.4 = 49.6
Answer: E
Answer: (E) 49.6
Question: On a sum of money, the simple interest for 2 years is Rs. 330, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is
(A) 15%
(B) 14.25%
(C) 6.06%
(D) 10.5%
(E) 11.5%
Rationale: Explanation:
The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
= (R Ã— SI)/(2 Ã— 100)
Difference between the compound interest and simple interest = 340 - 330 = 10
(R Ã— SI)/(2 Ã— 100) = 10
(R Ã— 330)/(2 Ã— 100) = 10
R = 6.06%
Answer: Option C
Answer: (C) 6.06%
Question: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B. Which of the following can be the difference of A and B ?
(A) 73
(B) 44
(C) 27
(D) 21
(E) 91
Rationale: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B:
A = 10x + y
B = 10y + x
A - B = (10x + y) - (10y + x) = 9(x - y). As you can see the difference must be a multiple of 9. Only option C is a multiple of 9.
Answer: C.
Answer: (C) 27
Question: y = 2x^2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
(A) -120.5
(B) -124.5
(C) -128.5
(D) -132.5
(E) 132.5
Rationale: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form of ax^2+bx+c=0,
The product of the roots =c/a= 256/2=128 and the sum of the roots =-b/a=-b
128 can be expressed as product of two numbers in the following ways:
1 * 256
2 * 128
4 * 64
8 * 32
16 * 16
The sum of the roots is maximum when the roots are 1/2 and 128 and the maximum sum is 1/2 + 128 = 128.5
The least value possible for b is therefore -128.5.
C
Answer: (C) -128.5
Question: Alice leaves her home and walks toward Bob's house. One hour later, Bob leaves his home and walks toward Alice's house. The distance between their homes is 41 kilometers, Alice's walking speed is 5 km/h, and Bob's walking speed is 4 km/h. How many kilometers will Alice walk before she meets Bob?
(A) 22
(B) 25
(C) 27
(D) 38
(E) 30
Rationale: Alice walks 5 km in the first hour so there are 36 km remaining.
When Bob starts walking, they complete a total of 9 km per hour.
They will meet four hours after Bob starts walking.
Since Alice walks for 5 hours, she walks 25 km.
The answer is B.
Answer: (B) 25
Question: Which of the following fractions, if written as a decimal, would have a 2 in the thousandths place ?
(A) 3/11
(B) 7/9
(C) 1/8
(D) 4/7
(E) 1/6
Rationale: Here rewriting the fractions
A)0.2727272727272727...
B)0.777777
C)0.25
D)0.5714285...
E)0.1666666
Clearly A will be our pick as the thousandths digit is 2
Hence A
Answer: (A) 3/11
Question: A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: ‘Exactly n of the statements on this sheet are false.’ Which statements are true and which are false?
(A) The even numbered statements are true and the odd numbered statements are false.
(B) The odd numbered statements are true and the even numbered statements are false.
(C) All the statements are false.
(D) The 39th statement is true and the rest are false
(E) The 69th statement is true and the rest are false
Rationale: Assume there is only one statement is there. The statement should read "Exactly 1 statement on this sheet is false" . If the truth value of the statement is true, then given statement should be false. This is contradiction. If the statement is false, Then the given statement is true. but there is not other true statement.
Assume there are two statements. By the above logic, 2nd statement should not be true. But 1st statement is true as it truthfully says the truthfulness. By this logic we know that If there are "n" statements, (n-1)th statement is the only true statement And all other are false
Answer:B
Answer: (B) The odd numbered statements are true and the even numbered statements are false.
Question: A train covers a certain distance at a speed of 200kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
(A) 400 km/hr
(B) 420 km/hr
(C) 450 km/hr
(D) 470 km/hr
(E) 580 km/hr
Rationale: Explanation:
Distance = 200×4 = 800km
Required speed = (800/2) = 400km/hr
Answer: Option A
Answer: (A) 400 km/hr
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
(A) 99
(B) 277
(C) 12
(D) 989
(E) 221
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: C
Answer: (C) 12
Question: There are 13 which, 15 black, 16 red hats on a table. In one step, you may chose two hats of different colors and replace each one by a hat of the third color. After how many steps this can be reached?
(A) 2
(B) 7
(C) 3
(D) 9
(E) 1
Rationale: Let the initial number of hats are (a, b, c). In one step the hats color may change into one of the following (a+2, b-1, c-1), (a-1, b+2, c-1), (a-1, b-1, c+2). In each of these cases, difference between any two colored hats should be divisible by 3 to reach mono chromatic stage. ie., a + b + c should also be divisible by 3.
In this case sum is not divisible by 3 so the final stage cannot be reached.
Answer:C
Answer: (C) 3
Question: A row of ants comprised of 102 ants. A man walked upon it and all except 42 were crushed beneath his foot.
How many ants are left alive?
(A) 41
(B) 42
(C) 43
(D) 44
(E) 45
Rationale: Solution:
All except 42 were crushed means that all the ants except 42 were crushed beneath the man's foot. Hence, 42 ants are alive now
Answer B
Answer: (B) 42
Question: John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make aprofit.
(A) Rs. 90
(B) Rs. 120
(C) Rs. 200
(D) Rs. 250
(E) Rs. 290
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Answer: (C) Rs. 200
Question: If x > 2000, then the value of (x)/(2x+1) is closest to?
(A) 1/6
(B) 1/3
(C) 10/21
(D) 1/2
(E) 3/2
Rationale: assume x = 1999
(x)/(2x+1) = 1999 / (1999*2+1)
=1999 / 3999
= = 1/2
Ans - D
Answer: (D) 1/2
Question: If the cost price is 91% of sp then what is the profit %
(A) 9.89%
(B) 8.90%
(C) 9.00%
(D) 8.00%
(E) 9.27%
Rationale: Sol. sp=Rs100 : then cp=Rs 91:profit =Rs 9.
Profit={(9/91)*100}%=9.89%
Answer is A.
Answer: (A) 9.89%
Question: In a race of 2.4 Kms. A beats B by 400 m or 20 sec. What is A’s time over the course?
(A) 1 min 30 sec
(B) 1 min
(C) 1 min 10 sec
(D) 1min 40 sec
(E) 1min 50 sec
Rationale: 2400*20/400=120
120-20=100sec=1 min 40 sec.
ANSWER:D
Answer: (D) 1min 40 sec
Question: On a certain road, 40% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 15%
(D) 22%
(E) 50%
Rationale: suppose there are X motorists.
40% of them exceeded the speed limit and received the ticket, i.e. 2X/5.
Again, suppose total no. of motorists who exceeded the speed limit are Y.
20% of Y exceeded the speed limit but didn't received the ticket, i.e. Y/5.
it means 4Y/5 received the ticket.
hence, 4Y/5 = 2X/5
or Y/X=1/2
or Y/X * 100= 1/2 * 100= 50%
E
Answer: (E) 50%
Question: Tanks C and B are each in the shape of a right circular cylinder. The interior of tank C has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank C is what percent of the capacity of tank B?
(A) 75%
(B) 80%
(C) 100%
(D) 120%
(E) 125%
Rationale: B.
For C, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
C/B = 160pi/200pi = 0.8
Answer: (B) 80%
Question: A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people, the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people be solicited?
(A) 300
(B) 250
(C) 400
(D) 500
(E) None
Rationale: Solution: Let the number of people be x who has been asked for the donations.
People already solicited = 60% of x = 0.6x
Remaining people = 40% of x = 0.4x
Amount collected from the people solicited,
= 600 *0.6x = 360x
360x = 75% of the amount collected.
Remaining amount = 25% = 120x
Thus,
Average donations from remaining people,
= 120x /0.4x = 300.
Answer: Option A
Answer: (A) 300
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
(A) 4: 45 p.m.
(B) 5: 00 p.m.
(C) 5: 20 p.m.
(D) 5: 35 p.m
(E) 6: 00 p.m
Rationale: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 3:20 +2=5:20
ANSWER:C
Answer: (C) 5: 20 p.m.
Question: A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?
(A) 12 cm
(B) 10 cm
(C) 83 cm
(D) 20 cm
(E) 30 cm
Rationale: 30 * 20 * x
= (8 * 5.5 * 1.5)/2=10
Answer:B
Answer: (B) 10 cm
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
(A) 2 hours
(B) 7 hours
(C) 8 hours
(D) 3 hours
(E) 3 hours
Rationale: |-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer:A
Answer: (A) 2 hours
Question: Find the mean proportional of the following pairs of numbers 6 and 24.
(A) 27
(B) 28
(C) 29
(D) 23
(E) 12
Rationale: Required number of trees
= 24/36 * 42
= 28.
Answer:B
Answer: (B) 28
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 12m/h. what is the speedof the person while he was going to his office?
(A) 8km/h
(B) 12km/h
(C) 14km/h
(D) 16km/h
(E) 17km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=12
\inline \Rightarrow 1.5k = 12
\inline \Rightarrow k=8km/h
A
Answer: (A) 8km/h
Question: 5 men and 3 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
(A) 1:1
(B) 1:3
(C) 2:1
(D) 2:3
(E) None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 5x + 3y = 4(x+y)
=> x = y
=> x/y = 1/1
=> x:y = 1:1
Option A
Answer: (A) 1:1
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 3 inches long, how wide is Jordan's rectangle, in inches?
(A) 25
(B) 43
(C) 42
(D) 40
(E) 18
Rationale: Area of Carol's rectangle = 24*5 = 120
Let width of Jordan's rectangle= w
Since , the areas are equal
3w = 120
=>w = 40
Answer D
Answer: (D) 40
Question: Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
(A) 99
(B) 88
(C) 71
(D) 18
(E) 77
Rationale: 93 + 123 + 153 = a3 => a = 18
Answer: D
Answer: (D) 18
Question: Two planes take off from neighboring runways at the same time. The British Airways Jet heads directly East at 300 Km/Hr, while the American Airlines Jet takes off heading directly west at 250km/hr. At this speed, how long before the two planes are 2,000 Km away from each other?
(A) 4 hours
(B) 3.75 hours
(C) 3.0 hours
(D) 3.5 hours
(E) 3.63 Hours
Rationale: For every hour the planes travel in opposite directions, they are 550 Km away from each other. So to be 2,000 Km away, it would take (2,000 Km/550 Km/Hour= 3.63 Hours).
Answer is E
Answer: (E) 3.63 Hours
Question: If the sum of a number and its square is 210, What is the number?
(A) 16
(B) 14
(C) 25
(D) 87
(E) 171
Rationale: Explanation:
Let the integer be x.
Then, x + x2 = 210
x2 + x - 210 = 0
(x + 15) (x – 14) = 0
x = 14
ANSWER: B
Answer: (B) 14
Question: During a clearance sale, a retailer discounted the original price of its TVs by 30% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
(A) 40%
(B) 45%
(C) 56%
(D) 60%
(E) 62.5%
Rationale: VERITAS PREPOFFICIAL SOLUTION:
C With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 30% off means that customers will pay 70% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 70% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 70% sale price. Using fractions, that means they pay: 4/5*(0.7) of the original price, which nets to 0.56 of the original price, or 56%.
Answer: (C) 56%
Question: 80 370 860 ? 2440 3530
(A) 900
(B) 840
(C) 750
(D) 860
(E) 1550
Rationale: 10^2 - 20 = 80
20^2 - 30 = 370
30^2 - 40 = 860
40^2 - 50 = 1550
50^2 - 60 = 2440
60^2 - 70 = 3530.
ANSWER:E
Answer: (E) 1550
Question: In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 9 women?
(A) A)144
(B) B)15
(C) C)20
(D) D)18
(E) E)21
Rationale: Required number of ways = 4C3*9C2 = 4*36 = 144
Answer is A
Answer: (A) A)144
Question: Average of first five multiples of 10 is
(A) 9
(B) 11
(C) 30
(D) 15
(E) 17
Rationale: Explanation:
Average=10(1+2+3+4+5) / 5=150 / 5=30
Option C
Answer: (C) 30
Question: Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 60 percent was planted with grapes and 30 percent of the cleared land was planted with potato. If the remaining 360 acres of cleared land was planted with tomato, how many acres did the farmer own?
(A) 3250
(B) 3450
(C) 4000
(D) 3750
(E) 3800
Rationale: 60% of 90% = 54%, 30% 0f 90% = 27% so the remaining 90-54-27=9%=360 acres or 10% of 90%=9% --> 360/9*100=4000 acres Answer (C)
Answer: (C) 4000
Question: There are 2 friends Peter and Paul. Peter age is twice as old as Paul when peter was as old as Paul is now. Sum of the present ages of Peter and Paul is 35.What is the present age of Peter?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: let pauls age be 'a' and peters be 'e'
e+a=35 (given)
e=35-a ------eq1
when peter was as old as paul that is when peter's age was 'a'
pauls age was a-(e-a) =2a-e
now peters age is e=2(2a-e)
e=4a-2e
3e=4a
3(35-a)=4a
105-3a=4a
a=15
hence e=20
ANSWER:C
Answer: (C) 20
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 1/7
(B) 1/8
(C) 1/9
(D) 7/8
(E) 1/5
Rationale: Original share of 1 person = 1/8
New share of 1 person = 1/7
Increase =(1/7-1/8) = 1/56
Required fraction = (1/56)/(1/8)
= (1/56)*8
= 1/7
ANSWER:A
Answer: (A) 1/7
Question: The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 200 terms of the sequence?
(A) 201/100
(B) 99/100
(C) 100/101
(D) 1/10000
(E) 200/201
Rationale: Easy task and accomplish
X1=1-1/2
x2=1/2-1/3
x3=1/3-1/4
.....
x199=1/199-1/200
x200=1/200-1/201
sum=X1+X2+X3+....X200=1-1/2+1/2-1/3+.......1/199-1/200+1/200-1/201=1-1/201=200/201
E is the answer
Answer: (E) 200/201
Question: In a mixture of 60 litres the ratio of milk to water is 5:1. Additional 20 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
(A) 2:3
(B) 5:3
(C) 1:4
(D) 3:2
(E) 3:1
Rationale: Given that Milk/Water=5x/x and 5x+x=60 --> x=10.
Thus Milk=5x=50 liters and Water=x=10 liters.
New ratio = 50/(20+10) = 50/30 = 5/3.
Answer is B
Answer: (B) 5:3
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 2.9 hrs
(B) 8.9 hrs
(C) 2.9 hrs
(D) 7.2 hrs
(E) 8.6 hrs
Rationale: Net part filled in 1 hour = (1/4 - 1/9)
= 5/36
The cistern will be filled in 36/5 hrs i.e., 7.2 hrs.
Answer:D
Answer: (D) 7.2 hrs
Question: If (10^67) – 63 is written as a base 10 integer, which of the following options is the sum of the digits in that integer?
(A) 598
(B) 495
(C) 590
(D) 595
(E) 695
Rationale: We know that (10^67) is ending 00, so (10^67) – 63=9....9937
total number of digits in (10^20) – 63 is 67, or 65 digits of 9 and two digits 3 and 7.
answer choice is 65*9+10=595
Answer is D 595
Answer: (D) 595
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 1/8; circuit two, 3/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
(A) 9/80
(B) 3/10
(C) 35/80
(D) 303/800
(E) 497/800
Rationale: The first circuit doesn't matter.
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 9/80 = 71/80
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (71/80)(7/10) = 1 - 497/800 = 303/800
D
Answer: (D) 303/800
Question: Effective annual rate of interest corresponding to nominal rate of 6% per annum compounded half yearly will be
(A) 6.09%
(B) 6.10%
(C) 6.12%
(D) 6.14%
(E) None of these
Rationale: Explanation:
Let the amount Rs 100 for 1 year when compounded half yearly, n = 2, Rate = 6/2 = 3%
Amount=100(1+3/100)2=106.09
Effective rate = (106.09 - 100)% = 6.09%
Option A
Answer: (A) 6.09%
Question: If the average (arithmetic mean) of x + 1, x + 4, and x + 7 is 0, then x =
(A) –4
(B) –3
(C) –2
(D) –1
(E) 0
Rationale: (x+1 + x+4 + x+7)/3 = 0
=>3x + 12 = 0
=>x = -4
Answer A
Answer: (A) –4
Question: Find the average of first 20 natural numbers.
(A) A)11.5
(B) B)20.5
(C) C)10.5
(D) D)15.5
(E) E)21.9
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 20 natural numbers = 20*21/2 =210
average = 210/20 = 10.5
Answer is C
Answer: (C) C)10.5