mathewhe/aqua_rat huggingface dataset:
Question: Jaclyn buys $60 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter
(A) 1187.5
(B) 1234
(C) 1289
(D) 1425
(E) None of these
Rationale: Explanation:
I=(p x r x t)/100
= 60000*9.5/100*(18/12)^1/6 = 1425
Answer: D
Answer: (D) 1425
Question: Exactly 18% of the reporters for a certain wire service cover local politics in Country X. If 40% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
(A) 20%
(B) 42%
(C) 44%
(D) 70%
(E) 84%
Rationale: Let's assume there are 100 reporters --> 18 reporters cover local politics.
Now, as 40% of the reporters who cover all politics do not cover local politics then the rest 60% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 60% of them equal to 18 (# of reporters who cover local politics): 0.6x=18 --> x=30, hence 30 reporters cover politics and the rest 100-30=70 reporters do not cover politics at all.
Answer: D.
Answer: (D) 70%
Question: A local bank that has 15 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 15 codes?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Consider the code XY. If there are nn digits available then X can take nn values and Y can also take nn values, thus from nn digits we can form n2n2 different 2-digit codes: this is the same as from 10 digits (0, 1, 2, 3, ..., 9) we can form 10^2=100 different 2-digit numbers (00, 01, 02, ..., 99).
We want # of codes possible from nn digit to be at least 15 --> n2≥15n2≥15 --> n≥4n≥4, hence min 4 digits are required.
Answer: B.
Answer: (B) 4
Question: Solution Y is 30 percent liquid P and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid P?
(A) 30%
(B) 33 1/3%
(C) 37 1/2%
(D) 40%
(E) 50%
Rationale: Answer:C
Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid P and 70% water, and then I was able to get the answer. That was a bit tricky and nice question=C
Answer: (C) 37 1/2%
Question: Machine T can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A)  1/2
(B)  1/3
(C)  4/13
(D)  8/29
(E)  6/33
Rationale: Let the following be true:
T makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C
Answer: (C)  4/13
Question: If all the numbers 2, 3, 4, 5, 6, 7, 8 are arranged, find the number of arrangements in which 2, 3, 4, are together?
(A) 650
(B) 680
(C) 720
(D) 740
(E) 750
Rationale: If (2 3 4) is one.
we must arrange (2 3 4), 5, 6, 7, 8 in
5P5 = 5! = 120 ways
2, 3, 4 can be arranged in 3P3 = 3! = 6
120 × 6 = 720.
C
Answer: (C) 720
Question: The average of first 10 natural numbers is?
(A) 5.9
(B) 5.5
(C) 5.4
(D) 5.1
(E) 5.2
Rationale: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer: B
Answer: (B) 5.5
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
(A) 60 kmph
(B) 5 kmph
(C) 10 kmph
(D) 15 kmph
(E) 120 kmph
Rationale: Explanation:
Let speed of the car be x kmph.
Then, speed of the train =150/100x=(3/2x)kmph
75/x-75/(3/2)x=125/10*60
75/x-50/x=5/24
x=(25*24/5)=120 kmph
ANSWER:E
Answer: (E) 120 kmph
Question: How long will take a leak at the bottom of a tank to empty it if it will take
8 hours to fill it without the leak, but due to the leak it will take 9 hours to be filled?
(A) 50 hours
(B) 33 hours
(C) 72 hours
(D) 82 hours
(E) 92 hours
Rationale: Part filled without leak in 1 hour = 1/8
Part filled with leak in 1 hour = 1/9
Work done by leak in 1 hour
=1/8âˆ’1/9=72 hours
Answer:C
Answer: (C) 72 hours
Question: The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
(A) 3000
(B) 2802
(C) 1750
(D) 2990
(E) 2982
Rationale: C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8)
= Rs.1750
Answer:C
Answer: (C) 1750
Question: Which of the following options represents an approximate value for the question mark (?) in the following equation? 662.4 + 15.2 × 4.1 + ? = 672.951
(A) 71.9
(B) 74.9
(C) 76.9
(D) 77.9
(E) 72.9
Rationale: 662.4 + 15.2 × 4.1 + ? = 672.951
or, ? = 672.951 – 662.4 + 15.2 × 4.1
? = 672.951 – 662.4 + 62.32
≈ 72.9
Answer E
Answer: (E) 72.9
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
(A) 7
(B) 8
(C) 5
(D) 4
(E) 10
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25 => x = 5
Hence, B's age = 2x = 10 years.
ANSWER E
Answer: (E) 10
Question: When 1/10 percent of 6,000 is subtracted from 1/10 of 6,000, the difference is
(A)  0
(B)  50
(C)  450
(D)  495
(E)  694
Rationale: We can break this problem into two parts:
1) What is 1/10 percent of 6,000?
2) What is 1/10 of 6,000?
To calculate 1/10 percent of 6,000 we must first remember to DIVIDE 1/10 BY 100.
So we have: (1/10)/(100)
To divide a number by 100 means to multiply it by 1/100, so we have:
1/10 x 1/100 = 1/1,000
Thus, 1/10 percent of 6,000 = 1/1,000 x 6,000 = 6.
Now let's concentrate on part 2. We need to calculate 1/10 of 5,000. To do this we simply multiply 1/10 by 6,000.
1/10 x 6,000 = 600
The answer to part 1 is 6, and the answer to part 2 is 600. Their difference is 600 – 6 = 694.
Answer E.
Answer: (E)  694
Question: A sum was put at simple interest at a certain rate for 7 years Had it been put at 2% higher rate, it would have fetched 140 more. Find the sum.
(A) 500
(B) 750
(C) 1000
(D) 1250
(E) 1500
Rationale: Difference in S.I. = P×T/100(R1−R2)
⇒ 140 = P×7x2/100(∵ R1 - R2 = 2)
⇒ P = 140×100/7×2=1000
Answer C
Answer: (C) 1000
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
(A) 22
(B) 77
(C) 23
(D) 44
(E) 51
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer: C
Answer: (C) 23
Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 30 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?
(A) 20%
(B) 40%
(C) 50%
(D) 62.5%
(E) 75%
Rationale: original SP = X
Cost =C
current selling price = .8x ( 20% discount)
.8x = 1.3C (30% profit)
x= 1.3/.8 *C
x= 13/8 C
Original selling price is 1.625C which is 62.5% profit
Answer D
Answer: (D) 62.5%
Question: What was the day of the week on, 18th July, 1776?
(A) Thursday
(B) Wednesday
(C) Monday
(D) Saturday
(E) SUNDAY
Rationale: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days)
Total number of odd days = (0 + 4) = 4.
Required day was 'Thursday'.
Answer:A
Answer: (A) Thursday
Question: If a2 - b2 = 10 and a*b = 8, find a4 + b4.
(A) 200
(B) 228
(C) 182
(D) 102
(E) 128
Rationale: a2 - b2 = 10 : given
a4 + b4 - 2a2b2 = 102 : square both sides and expand.
a*b = 8 : given
a2b2 = 82 : square both sides.
a4 + b4 - 2(64) = 100 : substitute
a4 + b4 = 228
correct answer B
Answer: (B) 228
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 38 seconds
(B) 26 seconds
(C) 88 seconds
(D) 12 seconds
(E) 18 seconds
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.
Answer:D
Answer: (D) 12 seconds
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/5 %, then the amount invested at 11% was?
(A) 23777
(B) 30000
(C) 29977
(D) 26777
(E) 19871
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 48/5 * 1/100)
(9x + 1100000 - 11x) = 960000
x = 70000
Sum invested at 9% = Rs. 70000
Sum invested at 11% = Rs. (100000 - 70000) = Rs. 30000.
Answer: B
Answer: (B) 30000
Question: The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 255
(B) 267
(C) 245
(D) 277
(E) 215
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (160 + x)/30 = 25/2 => 2(160 + x) = 750 => x = 215 m.
Answer:E
Answer: (E) 215
Question: What number when divided in half becomes zero ?
(A) 2
(B) 4
(C) 9
(D) 6
(E) 8
Rationale: E
8 is the required number.
Here, by dividing in half, we will actually chop off the digit from the middle. Then you will be left with two zeroes.
Answer: (E) 8
Question: Calculate the distance covered by 320 revolutions of a wheel of radius 28.1 cm.
(A) 465.2 m
(B) 965.2 m
(C) 265.2 m
(D) 565.2 m
(E) 165.2 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 320 * 2 * 22/7 * 28.1 = 56521.14 cm = 565.2 m
ANSWER:D
Answer: (D) 565.2 m
Question: A rectangular field has to be fenced on three sides leaving a side of 2020 feet uncovered. If the area of the field is 680680 sq. feet, how many feet of fencing will be required?
(A) 95
(B) 92
(C) 88
(D) 82
(E) 80
Rationale: Explanation:
Area of the field =680 sq. feet.
Length of the adjacent sides are
20 feet and 680/20=34 feet.
Required length of the fencing
=20+34+34=88 feet
Answer: Option C
Answer: (C) 88
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 8 hours
(B) 10 hours
(C) 12 hours
(D) 24 hours
(E) none of the above
Rationale: A's 1 hour's work = 1/4 ;
(B + C)'s 1 hour's work = 1/3 ;
(B + C)'s 1 hour's work = 1/2
(A + B + C)'s 1 hour's work = (1/4 + 1/3) = 7/12
B's 1 hour's work = (7/12 - 1/2) = 1/12
B alone will take 12 hours to do the work.
Answer = C
Answer: (C) 12 hours
Question: What is the sum of natural numbers between 60 and 100
(A) 4800
(B) 4860
(C) 5000
(D) 5500
(E) 3280
Rationale: a = first number
l = last number
Sn = n/2[a + l]
between 60 and 100 numbers = 41 => 100 - 60 = 40 + 1 = 41
Sn = 41/2 Ã— 160 = 41 Ã— 80 = 3280
Answer : E
Answer: (E) 3280
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 130 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 55
(B) 65
(C) 75
(D) 85
(E) 95
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 130 + P
C + M = 130
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 130/2 = 65.
ANSWER:B
Answer: (B) 65
Question: A table is bought for Rs.400/- and sold at Rs.300/- find gain or loss percentage
(A) 25% loss
(B) 20% gain
(C) 20% loss
(D) 15% gain
(E) None
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (300 - 400)/400 = 25% loss
A
Answer: (A) 25% loss
Question: Joseph Paul and his friend went for fishing.
They got six fishes without heads, nine fishes without the tail and eight fishes cut in two halves.
How many fishes did they caught ?
(A) 0
(B) 4
(C) 1
(D) 7
(E) 5
Rationale: A
6 without head => 0
9 without tail => 0
8 in two halves => 0 & 0
Answer: (A) 0
Question: A green lizard can travel from the green cave to the blue cave in 108 minutes; the blue lizard can travel from the blue cave to the green cave in 25% less time. If the green lizard started to travel 7.5 minutes before the blue lizard, how many minutes after the blue lizard, will the green lizard pass the middle line?
(A) 2.
(B) 3.5.
(C) 4.
(D) 5.5.
(E) 6.
Rationale: Time take by the green lizard to cover the distance between the caves = 108 mins
Time take by the green lizard to cover half the distance = 108/2 = 54 mins
Time take by the blue lizard to cover the distance between the caves = 108 x 3/4 =81 mins
Time take by the blue lizard to cover half the distance = 81/2 = 40.5 mins
Now the green lizard had been travelling for 7.5 mins when the blue lizard started. Therefore when the blue lizard starts to move the green lizard will have to cover 54 - 7.5 = 46.5 mins worth of distance at its current speed.
Difference in time when they both reach the mid point = 46.5 - 40.5 = 6mins.
E IS THE CORRECT ANSWER.
Answer: (E) 6.
Question: If 40% of a certain number is 160, then what is 60% of that number?
(A) 270
(B) 380
(C) 260
(D) 360
(E) 240
Rationale: Explanation:
40% = 40*4 = 160
60% = 60*4 = 240
Answer: Option E
Answer: (E) 240
Question: Working simultaneously and independently at an identical constant rate, 6 machines of a certain type can produce a total of x units of product P in 10 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 5x units of product P in 6 days?
(A) 50
(B) 18
(C) 16
(D) 12
(E) 8
Rationale: 6 machines do x units in 10 days
we have x/10 => rate of the 6 machines
we know that we need to have 5x units in 6 days
therefore, we need to get to 5x/6 rate of the machines.
rate of one machine is x/10*1/6 = x/60.
now, we need to know how many machines need to work simultaneously, to get 5x done in 6 days.
5x/6 work needs to be done by machines that work at x/60 rate.
let's assign a constant Y for the number of machines:
(x/60)*y = 5x/6
y = 5x/6 * 60/x
cancel 6 with 60, and x with x and get -> 50. Answer choice A
Answer: (A) 50
Question: Find the least number must be subtracted from 11070 so that remaining number is divisible by 22.
(A) 2
(B) 3
(C) 4
(D) 7
(E) 8
Rationale: On dividing 11070 by 22 we get the remainder 4, so 4 should be subtracted. Answer is A.
Answer: (A) 2
Question: The perimeter of one face of a cube is 28 cm. Its volume will be:
(A) 125cm3
(B) 343cm3
(C) 250cm3
(D) 625cm3
(E) None of these
Rationale: Explanation:
Edge of cude = 28/4 = 7 cm
Volume = a*a*a = 7*7*7 = 343 cm cube
Option B
Answer: (B) 343cm3
Question: If a2 + b2 + c2 = 213 and ab + bc + ca = 6, then a + b + c is
(A) 14
(B) 20
(C) 15
(D) 32
(E) 64
Rationale: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 213 and ab + bc + ca = 6,
(a + b + c)^2 = 213 + 2(6)
= 225
= 15^2
therefore: a + b + c = 15
ANSWER:C
Answer: (C) 15
Question: Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 20 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)?
(A) 16 km/hr
(B) 20 km/hr
(C) 24 km/hr
(D) 28 km/hr
(E) 32 km/hr
Rationale: Let the speed of the slower train be x m/s
Then, the speed of the faster train is 2x m/s
The relative speed is 3x m/s
(100 + 100)/20 = 3x
x = 10/3 m/s
So, the speed of the faster train is 20/3 = 20/3 * 18/5 = 24 km/hr
The answer is C.
Answer: (C) 24 km/hr
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 1:5
(C) 3:5
(D) 4:5
(E) 6:5
Rationale: The volume of the cone = (1/3)Ï€r2h
Only radius (r) and height (h) are varying.
Hence, (1/3)Ï€ may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
ANSWER A
Answer: (A) 2:5
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
C
Answer: (C) 12
Question: If p^2 = q^2, which of the following must be true?
(A) p =q
(B) p = −q
(C) p = |k|
(D) |p| = |q|
(E) p = −|q|
Rationale: Since p^2=q^2 we have 0=p^2 – q^2 =(p-q)*(p+q). So p=q or p=-q.
So only (A) and only (B) cannot be an answer.
The choice (C) tells us that k should be greater than or equal to 0.
Similarly the choice (E) tells us that k should be less than or equal to 0.
So neither (C) nor (E) cannot be the answer.
The answer is, therefore, (D).
Answer: (D) |p| = |q|
Question: In the manufacture of a certain product, 4 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
(A) 0.125%
(B) 0.2%
(C) 0.16%
(D) 1.25%
(E) 2.0%
Rationale: Percent of defective produced = 4%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(4/100)*100%
= (16/10000)*100%
= (16/100)%
= .16 %
Answer C
Answer: (C) 0.16%
Question: In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/4 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
(A) 3/4
(B) 11/15
(C) 7/10
(D) 1/6
(E) 2/15
Rationale: 1/5 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/4(equiped with cable tv) i.e. 1/4(1/5) = 1/20
therefore only video cassette recorder = 1/10 - 1/20 = 1/20
Total = 1/5+1/20+neither cable tv nor videocassette recorders
1 = 1/4 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-1/4 = 3/4
Hence A.
Answer: (A) 3/4
Question: The time on a clock is 20 minutes past 7. What is the angle between the hands of the clock?
(A) 60 degrees
(B) 100 degrees
(C) 80 degrees
(D) 50 degrees
(E) 120 degrees
Rationale: The hour hand rotates 360 degrees in twelve hours.
The hour hand rotates 30 degrees in one hour.
The hour hand rotates 5 degrees in ten minutes.
At this time, the hour hand has rotated 220 degrees.
The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.
At this time, the minute hand has rotated 120 degrees.
The difference is 220 - 120 = 100 degrees.
The answer is B.
Answer: (B) 100 degrees
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
(A) 1677
(B) 1683
(C) 2523
(D) 3363
(E) 3478
Rationale: L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683. Answer: Option B
Answer: (B) 1683
Question: On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80?
(A) 18%
(B) 21%
(C) 33.35
(D) 33.3%
(E) 37.5%
Rationale: let the total no of campers be 100
total amount = (25*110)+(35*80)+(40*65) = 2750+2800+2600= $8150
required percentage = (2800/8150)*100=33.35%
C
Answer: (C) 33.35
Question: If there are 8 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
(A) 32
(B) 24
(C) 56
(D) 448
(E) 540
Rationale: Firstly, there are 8 ways to choose 3 groups from the 4 groups. Hence 8C3.
Next, with the 3 groups chosen, there are 2^3 choices of choosing either one of the siblings.
Hence, the total number of ways are 8C3 * (2^3) = 448
D
Answer: (D) 448
Question: The length of rectangle is thrice its breadth and its perimeter is 80 m, find the area of the rectangle?
(A) 432 sq m
(B) 356 sq m
(C) 300 sq m
(D) 428 sq m
(E) 525 sq m
Rationale: 2(3x + x) = 80
l = 30 b = 10
lb = 30 * 10 = 300
ANSWER:C
Answer: (C) 300 sq m
Question: If wy + z = w(y + z), which of the following must be true?
(A)  x = 0 and z = 0
(B)  w = 1 and y = 1
(C)  w = 1 and z = 0
(D)  w = 1 or y = 0
(E)  w = 1 or z = 0
Rationale: wy + z = wy + wz
z = wz
case 1: z not= 0, w = z/z = 1
case 2: z = 0, 0 = w0 = 0
Combining 2 cases: w = 1 or z =0
E. is the answer.
Answer: (E)  w = 1 or z = 0
Question: The sum of present age of Abe and the age before 7 years is 37. Find the present age of Abe. What will be his age after 7 years?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
Rationale: Present age = x
Before 7yrs, y=x-7
After 7yrs, z=x+7
By the qn,
x+(x-7)=37
2x-7=37
2x=37+7
x=44/2
x=22
z=x+7
=22+7
=29
ANSWER:E
Answer: (E) 29
Question: . In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 65 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A)  50%
(B)  47%
(C)  54%
(D)  55%
(E)  57%
Rationale: Registered voters = 100
D = 60
R = 40
65% of D ( 60) = 39
20% of R ( 40 ) = 8
Total voter% of registered voters = 47 / 100
47% Ans B
Answer: (B)  47%
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 9 1/4 min
(B) 11 1/4 min
(C) 7 1/4 min
(D) 8 1/2 min
(E) 9 1/2 min
Rationale: 3/12 + x/15 = 1
x= 11 1/4
ANSWER:B
Answer: (B) 11 1/4 min
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine F is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine F can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
(A) 14
(B) 13
(C) 11
(D) 9
(E) 7
Rationale: 'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.
To finish a work say Machine F you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D
Answer: (D) 9