mathewhe/aqua_rat huggingface dataset:
Question: A cicketer bas a certain average for 10 innings, In the eleventh inning, he scorod 98 runs, thereby increasing his average by 6 runs. His new average is
(A) 18 runs
(B) 28 runs
(C) 48 runs
(D) 42 runs
(E) 32 runs
Rationale: Explanation:
Let average for 10 innings be x. Then,
(10x + 198)/11 = x + 6 => 11x + 66 = 10x + 98 => x = 32.
New average = (x + 6) = 48 runs.
Answer: E
Answer: (E) 32 runs
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
(A) 35 years
(B) 40 years
(C) 50 years
(D) None of these
(E) Cannot be determined
Rationale: EXPLANATION
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.
Husband’s present age = (90 – 50) years = 40 years.
Answer B
Answer: (B) 40 years
Question: A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 3.9
(B) 4.2
(C) 5.3
(D) 1.5
(E) 3
Rationale: M = 9
S = x
DS = 9 + x
US = 9 - x
9 + x = (9 - x)2
9 + x = 18 -2x
3x = 9
x = 3
Answer:E
Answer: (E) 3
Question: A store sells a certain product at a fixed price per unit. At the product's current price, w units cost a total of exactly $300. If the price were lowered by $5 from its current value, then w + 2n units would cost exactly $300; if the price were raised by $5, then w – n units would cost exactly $300. What is the value of w?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p w pw = 300
p-5 w+2n (p-5)(w+2n) = 300
p+5 w-n (p+5)(w-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So w = 20 satisfies all equations!!
Answer: (C) 20
Question: How long does a train 100 m long running at the speed of 80 km/hr takes to cross a bridge 142 m length?
(A) 10.7 sec
(B) 10.9 sec
(C) 10.1 sec
(D) 15.1 sec
(E) 12.7 sec
Rationale: Speed = 80 * 5/18
= 22.2 m/sec
Total distance covered
= 100 + 142 = 242 m.
Required time = 242/22.2 '
= 10.9 sec.
Answer:B
Answer: (B) 10.9 sec
Question: If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?
(A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
(B) Ram = Rs.2500, Shyam = Rs.500, Mohan = Rs.250
(C) Ram = Rs.1200, Shyam = Rs.1300, Mohan = Rs.750
(D) Ram = Rs.3500, Shyam = Rs.500, Mohan = Rs.250
(E) None
Rationale: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
ANSWER:A
Answer: (A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 44 degrees. Find the temperature on Friday?
(A) 65 degrees
(B) 73 degrees
(C) 36 degrees
(D) 34 degrees
(E) 74 degrees
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 44
Tu + W + Th = 192 -44 = 148
F = 184 – 148 = 36
Answer:C
Answer: (C) 36 degrees
Question: A cone of height 7 cm and base radius 3 cm is carved from a rectangular block of wood 10 cm * 5 cm * 2 cm. The percentage of wood wasted is
(A) 26 %
(B) 28 %
(C) 32 %
(D) 34 %
(E) None
Rationale: Sol.
Volume of the block = (10 * 5 * 2)cm³ = 100 cm³
Volume of the cone carved out = [1/3 * 22/7 * 3 * 3 * 7] cm³
= 66 cm³
∴ Wood wasted = (100 - 66)% = 34%.
Answer D
Answer: (D) 34 %
Question: How many minutes does the minute hand gain in every one hour?
(A) 55
(B) 60
(C) 65
(D) No gain
(E) None of these
Rationale: 55
ANSWER:A
Answer: (A) 55
Question: A candidate got 30% of the votes polled and he lost to his rival by 1760 votes. How many votes were cast?
(A) 4000
(B) 4100
(C) 4200
(D) 4300
(E) 4400
Rationale: Let x be the total number of votes.
0.3x + 1760 = 0.7x
0.4x = 1760
x = 1760/0.4 = 4400
The answer is E.
Answer: (E) 4400
Question: 75 boys can complete a work in 26 days.how many men need to complete twice the work in 20 days
(A) 160
(B) 195
(C) 180
(D) 190
(E) 200
Rationale: one man can complete the work in 26*75=1950days = one time work
to Complete the work twice it will be completed in
let M be the no. of worker assign for this therefore the eqn becomes
M*20=2*1950
M=195 workers
ANSWER:B
Answer: (B) 195
Question: When a Laptop is sold for Rs. 27000, the owner loses 10%. At what price must that Laptop be sold in order to gain 10%?
(A) 33,000
(B) 34,000
(C) 35,000
(D) 36,000
(E) 37,000
Rationale: 90 : 27000 = 110 : x
x = (27000 x 110)/90 = 33000.
Hence, S.P. = Rs. 33,000.
Answer: Option A
Answer: (A) 33,000
Question: Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. After 10 minutes, the water level decreases 16 meters. What is value of the radius in meters?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/6
(E) 1/8
Rationale: 10*0.31 = 3.1 = pi*R^2*h
R^2 = 3.1 / (pi*16) which is about 1/16
R = 1/4
The answer is C.
Answer: (C) 1/4
Question: At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.5 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day?
(A)  7
(B)  8
(C)  9
(D)  10
(E)  11
Rationale: After renting bowling shoes the person is left with $12.80-$0.5=$12.30, which is enough for 12.3/1.5<9=~8.
Answer: B.
Answer: (B)  8
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) 6∏ cm
(B) 8∏ cm
(C) 12∏ cm
(D) 16∏ cm
(E) None of these.
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∏ cm
Question: The number of new words that can be formed by rearranging the letters of the word 'KEYBOARD' is ?
(A) 34118
(B) 40319
(C) 20119
(D) 40139
(E) 38132
Rationale: Number of words which can be formed
= 8! - 1 = 40320 - 1
= 40319
Answer:B
Answer: (B) 40319
Question: (0.86)(power 3) - (0.1)(power 3)/ (0.86)(power 2) + 0.086 + (0.1)(power 2) is:
(A) 0.86
(B) 0.68
(C) 0.96
(D) 0.69
(E) 0.76
Rationale: Given expression
= (0.86) (power 3) - (0.1)(power 3) / (0.86)(power 2) + (0.86 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.86 - 0.1)
= 0.76
Answer is E
Answer: (E) 0.76
Question: In year Y imported machine tools accounted for 30 percent of total machine-tools sales in the United States, and Japanese imports accounted for 60 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 50x/9
(B) 60x/9
(C) 65x/9
(D) 70x/9
(E) 75x/9
Rationale: Sales of imported tools = 30% of the total sales = 0.30*{total} = 3{total}/10;
Sales of Japanese tools = 60% of the sales of imported tools = 3/5*3{total}/10 = 9{total}/50
Since the sales of of Japanese tools was x, then 9{total}/50 = x -->9{total} = 50 x
{total} = 50x/9
Answer: A
Answer: (A) 50x/9
Question: a factory produces 1 defective bulb out of 10 bulbs a yr. if it produces 870 bulbs a yr, how many defective bulbs are produced?
(A) 84
(B) 85
(C) 86
(D) 87
(E) 88
Rationale: 10 out of 1 is defective
20 out of 2 is defective
100 out of 10 is defective
and so on
800 out of 80 is defective
70 out of 7 is defective
80+7=87
ANSWER:D
Answer: (D) 87
Question: P is 20% more efficient than Q. P can complete a work in 22 days. If P and Q work together, how many days will it take to complete the same work?
(A) 8
(B) 11
(C) 12
(D) 15
(E) 16
Rationale: The work done by P in 1 day = 1/22
Let work done by Q in 1 day = q
q × (120/100) = 1/22
q = 100/(22×120) = 10/(22×12)
The work done by P and Q in 1 day = 1/22 + 10/(22×12) = 22/(22×12)= 1/12
P and Q together can do the work in 12 days.
The answer is C.
Answer: (C) 12
Question: How many 7 digit number contain number 3 ?
(A) 2748472
(B) 3748472
(C) 4748472
(D) 5748472
(E) 6748472
Rationale: total 7 digit no. = 9*10*10*10*10*10*10 = 9000000
not containing 3 = 8*9*9*9*9*9*9 = 4251528
total 7 digit number contain 3 = 9000 - 4251528 = 4748472
ANSWER:C
Answer: (C) 4748472
Question: In a certain city, 50% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
(A) a) 50%
(B) b) 53%
(C) c) 54%
(D) d) 55%
(E) e) 57%
Rationale: Let total voters = 100
so D= 50, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
46+8=54
54/100*100=54%
C
Answer: (C) c) 54%
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
(A) 51.25
(B) 51.29
(C) 51.22
(D) 51.24
(E) 51.21
Rationale: Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500) = Rs. 51.25.Answer:A
Answer: (A) 51.25
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
(A) 1/19
(B) 1/20
(C) 1/23
(D) 2/17
(E) 1/17
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
B)
Answer: (B) 1/20
Question: If X,Y is 10%,30% smaller than Z then how much percentage is Y greater than X?
(A) 12 1/2 %
(B) 13%
(C) 13 1/2%
(D) 14%
(E) 22 2/9%
Rationale: X = 90 %
Y = 70 %
Z = 100 %
X-Y/X × 100 = 20/90 × 100 = 22 2/9 % greater than X
E
Answer: (E) 22 2/9%
Question: The population of a town is 30000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?
(A) 4300
(B) 19200
(C) 5120
(D) 5230
(E) 5366
Rationale: 30000 × 80/100 × 80/100 = 19200
Answer ; B
Answer: (B) 19200
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
(A) 10000
(B) 28869
(C) 10002
(D) 18089
(E) 10004
Rationale: 100 * 100 = 10000
125 * 80 = 10000
Answer:A
Answer: (A) 10000
Question: A single discount equivalent to the discount series of 18%, 10% and 5% is?
(A) 29.36
(B) 29.89
(C) 31.86
(D) 31.4
(E) 31.1
Rationale: 100*(82/100)*(90/100)*(95/100) = 70.11
100 - 70.11 = 29.89
Answer: B
Answer: (B) 29.89
Question: A man can row 40 kmph in still water and the river is running at 10 kmph. If the man takes 1 hr to row to a place and back, how far is the place?
(A) 16.5 kmph
(B) 12.15 kmph
(C) 2.25 kmph
(D) 18.75 kmph
(E) None of these
Rationale: Explanation :
Let the distance be x
Speed upstream = (40 - 10) = 30 kmph
Speed downstream = (40 + 10) = 50 kmph
Total time taken = 1 hr
(x/50) + (x/30) = 1
⇒8x/150 = 1
⇒ x = 150/8 = 18.75 kmph. Answer : Option D
Answer: (D) 18.75 kmph
Question: Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 2 more revolutions than gear P?
(A) 4
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: Gear Q makes 30 more revolutions each 60 seconds.
The time to make 2 = 30/15 more revolutions is 60/15 = 4 seconds.
The answer is A.
Answer: (A) 4
Question: In a certain warehouse, 50 percent of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80 percent of the packages weigh at least 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds?
(A) 8
(B) 64
(C) 72
(D) 102
(E) 144
Rationale: If 80% of the packages weigh at least 25 pounds
This means that 20% of the packages weigh LESS THAN 25 pounds
Let T = TOTAL number of packages
So, 20% of T = # of packages that weigh LESS THAN 25 pounds
48 packages weigh LESS THAN 25 pounds
GREAT. So, 20% of T = 48
Rewrite to get: 0.2T = 48
Solve:T = 240
50% of the packages weigh less than 75 pounds
So, 50% ofT= number of packages that weigh less than 75 pounds
50% of240=120, so120packages weigh less than 75 pounds
OF THOSE120packages that weigh less than 75 pounds,48packages weigh less than 25 pounds.
So, the number of packages that weight BETWEEN 25 and 75 pounds =120-48= 72 = C
Answer: (C) 72
Question: Riya and Priya set on a journey. Riya moves eastward at a speed of 20kmph and Priya moves westward at a speed of 30 kmph.How far will be priya from Riya after 30 minutes
(A) 25kms
(B) 10kms
(C) 50kms
(D) 30kms
(E) 40kms
Rationale: total eastward distance= 20kmph*1/2hr=10 km
total westward distance= 30kmph*1/2hr=15 km
total distn betn them= 10+15=25km
ans 25km
ANSWER:A
Answer: (A) 25kms
Question: Find the value of 72514 x 9999 = m?
(A) 345434667
(B) 246465757
(C) 465767867
(D) 725077485
(E) 645354643
Rationale: 72514x 9999 = 72514x (10000 - 1)
= 72514 x 10000 - 72514 x 1
= 725140000 - 72514
= 725077485
D
Answer: (D) 725077485
Question: 75 65 85 55 45 85 35 ? ?
(A) 25 15
(B) 25 85
(C) 35 25
(D) 85 35
(E) 25 75
Rationale: 75-10=65
again 85
65-10=55
55-10=45
again 85
45-10=35
35-10=25
again 85
then answer is 25 ,85
ANSWER:B
Answer: (B) 25 85
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 220 kilometers?
(A) 4.5
(B) 5.5
(C) 6.5
(D) 7.5
(E) 8.5
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 220 kilometers?
220 ÷ 40 = 5.5 × 1 gallon = 5.5 gallons
correct answer B
Answer: (B) 5.5
Question: How many times the keys of a typewriter have to be pressed in order to write first 400 counting numbers?
(A) 2388
(B) 1092
(C) 2788
(D) 1192
(E) 1901
Rationale: Explanation:
1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
Answer: B
Answer: (B) 1092
Question: If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a three-percent vinegar solution, what was the concentration of the original solution?
(A) 19.3%
(B) 17%
(C) 16.67%
(D) 15.5%
(E) 12.5%
Rationale: Let X be the quantity of non-vinegar in the strong vinegar solution
Thus vinegar quantity will be 12 - X
When 50 ounces of water were added the percentage of vinegar becomes 3%, thus (12 - X)/62 = 3/100
From this equation X = 10.14
Answer (12-10.14)/12 = 15.5%
ANSWER:D
Answer: (D) 15.5%
Question: The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %?
(A) 18%
(B) 20.5%
(C) 30%
(D) 45%
(E) 12%
Rationale: 1800 ---- 370
100 ---- ? => 20.5%
Answer:B
Answer: (B) 20.5%
Question: Two diesel trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 10 sec
(B) 30 sec
(C) 40 sec
(D) 20 s
(E) 50 sec
Rationale: D
Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.
Answer: (D) 20 s
Question: If watches bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425. What is the greatest possible profit that might be made in selling eight watches?
(A) Rs 900
(B) Rs 800
(C) Rs 1,800
(D) Rs 2,800
(E) None of these
Rationale: Profit would be maximum if watches are brought for Rs 200 and sold for Rs 425
Profit = Rs (425 - 200) = Rs 225
Profit of 8 watches = Rs 225 x 8 = Rs 1,800
ANSWER:B
Answer: (B) Rs 800
Question: A box is being assembled to fit 3 different toys. There are 10 stuffed animals, 5 cars and 6 science kits to chose from. How many different toy boxes are possible?
(A) 31
(B) 21
(C) 300
(D) 25
(E) 50
Rationale: 10 x 5 x 6 = 300
Answer: C
Answer: (C) 300
Question: 9873 + x = 13800, then x is ?
(A) 3327
(B) 3237
(C) 3927
(D) 2337
(E) None of these
Rationale: Answer
x = 13800 - 9873 = 3927
Option: C
Answer: (C) 3927
Question: 6.006/3.003
(A) 0.002
(B) 0.02
(C) 0.2
(D) 20
(E) 2
Rationale: Answer is 2, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 6006/3003= 2
Answer E
Answer: (E) 2
Question: If two sides of a triangle are 10 and 8, which of the following could be the area of triangle?
1. 35
2. 48
3. 56
(A) a) 1 only
(B) b) 1 and 2 only
(C) c) 1 and 3 only
(D) d) 2 and 3 only
(E) e) 1, 2 and 3 only
Rationale: when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.
lets say base = 12 , height =8 (angle = 90)
maximum area = (1/2)*12*8 = 48 ( this is the same maximum area even when base is 8 and height is 12).
if we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.
C,D and E are ruled out.
1 and 3 are possible areas as their areas are less than 48.
Hence the answer is C.
Answer: (C) c) 1 and 3 only
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
(A) 144
(B) 125
(C) 130
(D) 160
(E) 158
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min
ANSWER A
Answer: (A) 144
Question: The greatest number by which the product of three consecutive multiples of 3 is always
(A) 54
(B) 81
(C) 162
(D) 243
(E) None of these
Rationale: Explanation:
3*6*9 = 162
Option C
Answer: (C) 162
Question: A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find:
a) The distance the car has covered.
b) The time that took it to get from C to B.
(A) 223
(B) 277
(C) 116
(D) 268
(E) 281
Rationale: From the statement of the problem we don't know if the 15 min stop in town C was planned or it was unexpected. So we have to consider both cases.
1st case. The stop was planned. Let us consider only the trip from C to B, and let xx be the number of hours the driver spent on this trip.
Then the distance from C to B is S=40⋅xS=40⋅x km. If the driver could use the initial route, it would take him x−3060=x−12x−3060=x−12 hours to drive from C to B. The distance from C to B according to the initially itinerary was (x−12)⋅32(x−12)⋅32 km, and this distance is 2828 km shorter than 40⋅x40⋅x km. Then we have the equation
(x−1/2)⋅32+28=40x(x−1/2)⋅32+28=40x
32x−16+28=40x32x−16+28=40x
−8x=−12−8x=−12
8x=128x=12
x=128x=128
x=148=112=13060=x=148=112=13060= 1 hr 30 min.
So, the car covered the distance between C and B in 1 hour and 30 min.
The distance from A to B is 3⋅32+128⋅40=96+60=1563⋅32+128⋅40=96+60=156 km.
2nd case. The driver did not plan the stop at C. Suppose it took xx hours for him to get from C to B. Then the distance is S=40⋅xS=40⋅x km. It took x−3060−1560=x−4560=x−34x−3060−1560=x−4560=x−34 h to drive from C to B. The distance from C to B is 32(x−34)32(x−34) km, which is 2828 km shorter than 40⋅x40⋅x, i.e.
32(x−34)+28=40x32(x−34)+28=40x
32x−24+28=40x32x−24+28=40x
4=8x4=8x
x=12hr⋅x=30min.x=12hr⋅x=30min. Then the time of the trip from C to B was 30 min. The distance covered equals 3⋅32+12⋅40=96+20=116km3⋅32+12⋅40=96+20=116km.
Answer:C
Answer: (C) 116
Question: The number of new words that can be formed by rearranging the letters of the word 'REDUCTION' is ?
(A) 362879
(B) 362889
(C) 120
(D) 5040
(E) 5039
Rationale: Number of words which can be formed
= 9! - 1 = 362880 - 1
= 362879
Answer:A
Answer: (A) 362879
Question: The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?
(A) 12
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: This is an A.P. in which a = 6, d = 6 and Sn = 1800
Then,	n	[2a + (n - 1)d] = 1800
2
n	[2 x 6 + (n - 1) x 6] = 1800
2
3n (n + 1) = 1800
n(n + 1) = 600
n2 + n - 600 = 0
n2 + 25n - 24n - 600 = 0
n(n + 25) - 24(n + 25) = 0
(n + 25)(n - 24) = 0
n = 24
Number of terms = 24.
E)
Answer: (E) 24
Question: For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is?
(A) between 2 and 20
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) greater than 40
Rationale: SOL:
Lets consider h(100):
=> 2*4*6*8.........*98*100
=> (2*1) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50)
=> (2^50) * (1*2*3*4........*49*50)
=> h(100) = (2^50) * (50!)
We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100).
But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50;
ANSWER:E
Answer: (E) greater than 40
Question: If a person throw 2 dice simultaneously then find the probability of the sum of dots is a prime number?
(A) 5/12
(B) 6/13
(C) 8/17
(D) 9/11
(E) 3/5
Rationale: If 2 dies are thrown E = event of getting a prime number = 15
total number of possible out comes = 36
probability = 15/36 = 5/12
Answer is A
Answer: (A) 5/12
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 228
(B) 267
(C) 800
(D) 297
(E) 127
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
Answer: (C) 800
Question: Find k if 64 ÷ k = 4.
(A) 8
(B) 16
(C) 24
(D) 36
(E) 40
Rationale: Since 64 ÷ k = 4 and 64 ÷ 16 = 4, then
k = 16
correct answer B
Answer: (B) 16
Question: On a map the distance between two mountains is 312 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 42 inch from the base of the mountain. How many km is he from the base of the mountain?
(A) 14.83
(B) 14.81
(C) 14.8
(D) 14.82
(E) 18.3
Rationale: Explanation:
Since 312 inch = 136 km
So 1 inch = 136/312 km
So 42 inch = (136 Ã— 42)/ 312 = 18.3 km
Answer: E
Answer: (E) 18.3
Question: How many keystrokes are needed to type numbers from 1 to 1000 on a standard keyboard?
(A) 2893
(B) 3000
(C) 5213
(D) 5642
(E) None of these
Rationale: Explanation :
While typing numbers from 1 to 1000, we have 9 single digit numbers from 1 to 9. Each of them requires one keystroke. That is 9 key strokes.
There are 90 two-digit numbers, from 10 to 99. Each of these numbers requires 2 keystrokes. Therefore, one requires 180 keystrokes to type the 2 digit numbers.
There are 900 three-digit numbers, from 100 to 999. Each of these numbers requires 3 keystrokes. Therefore, one requires 2700 keystrokes to type these 3 digit numbers.
And,1000 is a four-digit number which requires 4 keystrokes.
Hence, total 9+180+2700+4= 2893 keystrokes is required.
Answer : A
Answer: (A) 2893
Question: A person X working alone can complete a work in 5 days. A person Y completes the same amount of work in 10 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: The fraction of work completed in two days is 2/5 + 2/10 + 2/30 = 20/30
The fraction of work remaining is 1 - 20/30 = 10/30
The number of days required for Z is 10 days.
The answer is E.
Answer: (E) 10