mathewhe/aqua_rat huggingface dataset:
Question: The price of gasoline in the area where the Smith family lives is scheduled to increase by 5% next year. Since the Smith family cannot afford an increase in their fuel bill, how much will they have to reduce consumption to keep their cost the same?
(A) 6.14%
(B) None
(C) 5%
(D) 2.45%
(E) 4.76%
Rationale: Solution: Let the current fuel expense be represented by Rs. 100.
The cost of gasoline rises 5%. So, to buy same amount of fuel, they need to increase their expense,
= (100 + 5% of 100) = Rs. 105.
But, they want to keep fuel expense the same, so they have to cut Rs. by 5 to keep it to Rs. =100.
The % decrease in consumption is,
(5/105)*100 = 4.76%.
Mental Calculation Method;
100-----5%↑---→105------X%↓---→100.
Here, X = (5/105)*100 = 4.76%.
Answer: Option E
Answer: (E) 4.76%
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
(A) 76 ways
(B) 30 ways
(C) 16 ways
(D) 15 ways
(E) 19 ways
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3
= 30 ways.
Answer:B
Answer: (B) 30 ways
Question: Sam invested Rs. 3000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
(A) 2554.0
(B) 3387.0
(C) 2503.0
(D) 3307.5
(E) 16537.11
Rationale: P = Rs. 3000 ; R = 10% p.a. = 5% per half-year; T = 1 year
= 2 half-year
Amount = [3000 * (1 + 5/100)2]
= (3000 * 21/20 * 21/20)
= Rs.3307.50
Answer:D
Answer: (D) 3307.5
Question: In how many different ways can the letters of the word 'CORPORATMON' be arranged so that the vowels always come together?
(A) 40000
(B) 50000
(C) 50400
(D) 50700
(E) 60000
Rationale: The word 'CORPORATMON' has 11 letters. It has the vowels 'O','O','A','M','O' in it and
these 5 vowels should always come together. Hence these 5 vowels can be grouped
and considered as a single letter. that is, CRPRTN(OOAMO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and
rest of the letters are different.
Number of ways to arrange these letters = 7!2! = (7×6×5×4×3×2×1)/(2×1) = 2520
In the 5 vowels (OOAMO), 'O' occurs 3 and rest of the vowels are different.
Number of ways to arrange these vowels among themselves = 5!3! = (5×4×3×2×1)/(3×2×1) = 20
Hence, required number of ways = 2520 x 20 = 50400
C
Answer: (C) 50400
Question: A car traveled from San Diego to San Francisco at an average speed of 51 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
(A) 24.
(B) 34.
(C) 36.
(D) 42.
(E) 44.
Rationale: Let the time taken be = x
One way distance = 51x
Total distance traveled = 2 * 51x = 102x
Total time taken = x + 2x = 3x
Average speed = 102x/3x = 34
Answer: B
Answer: (B) 34.
Question: Analyze the number square carefully and find out what number fits in place of question mark.
35	20	14
9	17	42
2	8	?
(A) 12
(B) 6
(C) 18
(D) 2
(E) 42
Rationale: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(6
2/ 8) * 8 = 2*1= 2
D
Answer: (D) 2
Question: Three times the first of three consecutive odd integers is 6 more than twice the third. The third integer is:
(A) 9
(B) 11
(C) 13
(D) 15
(E) 18
Rationale: Let the three integers be x, x + 2 and x+ 4.
Then,
3x = 2(x + 4) + 6
x = 14
Third integer = x + 4 = 18.
ANSWER:E
Answer: (E) 18
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is?
(A) 39
(B) 28
(C) 27
(D) 69
(E) 71
Rationale: 1/2 * d (12 + 8) = 690
d = 69
Answer: D
Answer: (D) 69
Question: If each digit in the set of A = {1,2,3,4,5,6} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?
(A) 4*5!
(B) 6! - 5!
(C) 6! / 5!
(D) 6!* 5!
(E) 6! - 4!
Rationale: The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).
The number of ways to arrange 6 units is 6!
If we think of 2 and 5 as one single unit, the number of arrangements is 5!
Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*5!
The total number of valid arrangements is 6! - 2*5! = 6*5! - 2*5! = 4*5!
The answer is A.
Answer: (A) 4*5!
Question: A part of Rs. 38800 is lent out at 6% per 6 months. The rest of the amount is lent out at 5% per annum after 1 year. The ratio of interest after 3 years from the time when first amount was lent out is 5:4. Find the second part that was lent out at 5%.
(A) 28800
(B) 27800
(C) 29800
(D) 26500
(E) 55055
Rationale: Let the 1st part that is lent out be x at 6%. then 2nd part will be (38800-x) at 5%.then the S.I1 of 1st part is (p*r*t)/100 = (x*6*6)/100 [t=6 becoz we r calculating till 3yrs & der is six 6months in 3yrs]
similarly S.I2 of 2nd part = {(38800-x)*5*2}/100 [t=2 since the 5% rate is to be calculated after the 1st year & per annum, so no. of years left is 2]therefore, S.I1/S.I2=5/4, by calculating it we get x=10000So, 2nd part is 38800-10000=28800
ANSWER:A
Answer: (A) 28800
Question: A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
(A) 34
(B) 38
(C) 42
(D) 46
(E) 50
Rationale: 5/7*P are ponies with horseshoes, so P is a multiple of 7.
2/3*5/7*P = 10/21*P are Icelandic ponies with horseshoes, so P is a multiple of 21.
The minimum value of P is 21. Then H = P+4 = 25.
The minimum number of horses and ponies is 46.
The answer is D.
Answer: (D) 46
Question: Find The Missing Number in this sequence ?
1, 2, 6, 42, ? 3263442
(A) 2000
(B) 1806
(C) 4580
(D) 3546
(E) 1239
Rationale: B
1806
each number is multiplied by the number+1
1x2 = 2
2x3 = 6
6x7 = 42
42x43 = 1806
1806x1807 = 3263442
Answer: (B) 1806
Question: It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?
(A) 2 hours and 45 minutes.
(B) 5 hours and 45 minutes.
(C) 3 hours and 45 minutes.
(D) 4 hours and 45 minutes.
(E) 6 hours and 45 minutes.
Rationale: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = 3 hours and 45 minutes.
correct answer C
Answer: (C) 3 hours and 45 minutes.
Question: A boy is born when his father is 27 years old. How old will he be when he is exactly half his fathers' age?
(A) 23
(B) 24
(C) 25
(D) 27
(E) 39
Rationale: when son born:
son s=0
father f=27.
after x years:
son s=x
father f=f+x=27+x:
according to given condition
son age is exactly half his fathers' age...so
x=(27+x)/2---solve this
son age is 27
ANSWER:D
Answer: (D) 27
Question: A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by w meteres, What is the area of the rug in square meters?
(A) mn - p(m+n)
(B) mn – 2p(m+n)
(C) mn – p^2
(D) (m - p)(n - p)
(E) (m - 2p)(w - 2p)
Rationale: The answer must be E.
Plug in M 100
w 50
P 10.
Answer: (E) (m - 2p)(w - 2p)
Question: What is the sum of all the prime numbers from 20 to 40?
(A) 279
(B) 100
(C) 278
(D) 120
(E) 191
Rationale: Explanation:
23 + 29 + 31 + 37 = 120
Answer: D
Answer: (D) 120
Question: a company has 17 office tasks 8 outdoor tasks and 7 misc. tasks for workers each worker can complete 4 tasks max what is he minimum number of workers required
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Total subjects = 17+8+7=32
Max tasks by 1 worker = 4
So, min of workers required = 32/4 = 8
ANSWER:C
Answer: (C) 8
Question: Without stoppages, a train travels certain distance with an average speed of 80 km/h, and with stoppages, it covers the same distance with an average speed of 60 km/h. How many minutes per hour the train stops ?
(A) 15
(B) 18
(C) 10
(D) 16
(E) None of these
Rationale: Due to stoppages, it covers 20 km less .
Time taken to cover 20 km = 20⁄80h = 1⁄4h
= 1⁄4 × 60 min = 15 min
Answer A
Answer: (A) 15
Question: Which values of ‘x’ satisfies the inequality
x2 - 3x + 2 > 2x - 4 ?
(A) 2< x < 3
(B) x > 3 or x < 2
(C) x ³ 3
(D) x £ 2
(E) None of these
Rationale: Given expression is
x2 – 3x + 2 – 2x + 4 > 0
or, x2 – 5x + 6 > 0
or, x2 – 3x – 2x + 6 > 0
or, x(x – 3) – 2(x – 3) > 0
or, (x – 3)(x – 2) > 0
or, x > 3 or, x < 2
Answer B
Answer: (B) x > 3 or x < 2
Question: How many terms are in the G.P. 3, 6, 12, 24, ......., 96 ?
(A) 6
(B) 9
(C) 67
(D) 5
(E) 2
Rationale: Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 96 => a * r^(n-1) = 96
=> 3 * 2^(n-1) = 96 => 2^(n-1) = 32 = 2^(5)
=> n-1 = 5 => n = 6
Answer: A
Answer: (A) 6
Question: (x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. -6
II. -4
III. 2
IV. 3
(A) I and II only
(B) I and III only
(C) II and III only
(D) II and IV only
(E) II, III, and IV
Rationale: (x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only -4 and 2 satisfy both inequalities.
Answer: E.
Answer: (E) II, III, and IV
Question: The speed of a boat in still water is 60kmph and the speed of the current is 15kmph. Find the speed downstream and upstream?
(A) 80,47 kmph
(B) 75,55 kmph
(C) 80,42 kmph
(D) 80,40 kmph
(E) 83,40 kmph
Rationale: Speed downstream = 60 + 15 = 75 kmph
Speed upstream = 60 - 15 = 55 kmph.Answer:B
Answer: (B) 75,55 kmph
Question: If James has to pay 12 % interest per year on an amount of $60,000 for 12 year then what is total principal?
(A) 52000
(B) 24000
(C) 25000
(D) 27000
(E) 24590
Rationale: For simple interest, I = P * N * R / 100
let Principle P = x
I = x * 12 * 12 / 100
I = 1.44 * x
Amount = P + I
60000 = 1.44 x + x
x = 24590.16 = P
E
Answer: (E) 24590
Question: At a constant Rate of flow, it takes 30 minutes to fill a swimming pool if a large hose is used and 45 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
(A) 20
(B) 22
(C) 18
(D) 16
(E) 14
Rationale: time taken to fill the pool by Large Hose =30 minutes =L or 1/L=1/30 similarly 1/S=1/45
simultaneously it will take 1/L+1/S=1/30+1/45=5/90=18 minutes
Answer : C
Answer: (C) 18
Question: Working alone, A can complete a certain kind of job in 15 hours. A and D, working together at their respective rates, can complete one of these jobs in 10 hours. In how many hours can D, working alone, complete one of these jobs?
(A)  20
(B)  24
(C)  26
(D)  28
(E)  30
Rationale: Let total time taken by D to complete the job = D
total time taken by A to complete the job = 15
Work done by A in an hour
1/A = 1/15
Working together A and D can complete the job in 10 hours
1/A + 1/D = 1/10
=>1/D = 1/10 - 1/15
= 1/10 - 1/15
= 1/30
=> D = 30 hours
Answer E
Answer: (E)  30
Question: The area of a parallelogram is 128sq m.Then the area of a triangle formed by its diagonal is ----------?
(A) 128m
(B) 64m
(C) 64m^2
(D) 128m^2
(E) none
Rationale: b*h/2=128/2=64m. Ans:(B)
Answer: (B) 64m
Question: If X and Y are two different prime numbers, which of the following cannot be true?
(A) XY is odd.
(B) X + Y is even.
(C) X + Y is odd.
(D) XY is even.
(E) X/Y is an integer
Rationale: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (X/Y=integer means that X is a multiple of Y).
All other options are possible:
A. XY is odd --> X=3 and Y=5;
B. X + Y is even --> X=3 and Y=5;
C. X + Y is odd -->X=2 and Y=3;
D. XY is even --> X=2 and Y=3;
Answer: E.
Answer: (E) X/Y is an integer
Question: A trailer carries 3, 4 and 6 crates on a trip. Each crate weighs no less than 120 kg. What is the maximum weight of the crates on a single trip?
(A) 1250
(B) 625
(C) 600
(D) 7500
(E) 720
Rationale: Max No. of crates=6.
Max Weight=120Kg
Max. weight carried = 6*120=720Kg=E
Answer: (E) 720
Question: A 4-letter code word consists of letters H, I, and J. If the code includes all the three letters, how many such codes are possible?
(A) 72
(B) 48
(C) 18
(D) 24
(E) 36
Rationale: Note that the correct answer to this question is 36, not 72.
H-HIJ can be arranged in 4!/2!=12 ways;
I-HIJ can be arranged in 4!/2!=12 ways;
J-HIJ can be arranged in 4!/2!=12 ways;
Total: 12+12+12=36.
Answer: E
Answer: (E) 36
Question: A rectangular cube has sides measuring 3 inches long by 2 inches wide by 0.5 inches high. If the surface area of the rectangle is the same as a cube, what do the sides/walls of the cube measure? Round to the nearest whole number.
(A) 4
(B) 5
(C) 6
(D) 7
(E) 2
Rationale: First calculate the surface area of the rectangle by multiplying the length and width of the rectangle together, then multiply by 2 to get both sides of the rectangle. This calculates to 12 inches. Find the surface area of the sides of the rectangular cube. Multiply the height by the length of the rectangle. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 3 inches. Then multiply the width of the rectangle by the height. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 2 inches. Add the totals together to get the rectangular cube surface area of 17 inches. Since a square cube has 6 sides, divide the surface area by 6. This calculates to 2.833 inches as the surface area of each side of the cube. The square root of 2.833 is 1.683. Rounding to the nearest whole number that makes each side of the cube measuring 2 inches. The correct answer is (E).
Answer: (E) 2
Question: If the sum of the interior angles of a regular polygon measures up to 1260 degrees, how many sides does the polygon have?
(A) 6
(B) 3
(C) 9
(D) 4
(E) None of these
Rationale: 9 sides...answer is C
Answer: (C) 9
Question: 4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 4 days
(B) 6 days
(C) 7 days
(D) 9 days
(E) 1 days
Rationale: 1 women's 1 day work = 1/28
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/28 + 10/140) = 1/4
5 women and 10 children will complete the work in 4 days.
Answer: A
Answer: (A) 4 days
Question: Raja and Abdul can finish the work 18 days if they work together. They worked together for 12 days and then Abdul left. Rja finished the remaining work in another 12 days. In how many days Raja alone can finish the work?
(A) 30 days
(B) 60 days
(C) 70 days
(D) 36 days
(E) 90 days
Rationale: Amount of work done by Raja and Abdul in 1 day = 1/18
Amount of work done by Raja and Abdul in 12 days = 12 Ã— (1/18) = 2/3
Remaining work â€“ 1 â€“ 2/3 = 1/3
Raja completes 1/3 work in 12 days
Amount of work JOHN can do in 1 day = (1/3)/12 = 1/36
=>Raja can complete the work in 36 days
Answer : D
Answer: (D) 36 days
Question: A cube painted red on two adjecent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size.How many cubes are there which have no face painted?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: If a painted cube is cut into 64 (4^3) smaller cubes then there will be
i. smaller cubes with three face painted (cubes at the corner)= 8
ii.smaller cubes with two face painted (cubes at the edges)= (4-2)*12= 24
iii.smaller cubes with one face painted (cubes at the faces)= ((4-2)^2)*6=24
iv.smaller cubes not painted = 64-(8+24+24)= 8
ANSWER:A
Answer: (A) 8
Question: There are 4 numbers A, B, C, and D. If A:B = 1/2, B:C = 2/7, C:D = 7/3, then A:D will be?
(A) 1 : 2
(B) 2 :1
(C) 2 : 7
(D) 1 : 7
(E) 1 : 3
Rationale: Solution
A : B = 1 : 2, B : C = 2 : 7, C : D = 7 : 3
âˆ´Aâˆ¶Bâˆ¶Câˆ¶D= 1 : 2 : 7 : 3.
Thus, A : D = 1 : 3
Correct Option E
Answer: (E) 1 : 3
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
(A) 587 × 10<10>(exponent) miles
(B) 587 × 10<-12> (exponent) miles
(C) 587 × 10<-10>(exponent) miles
(D) 587 × 10<12>(exponent) miles
(E) 587 × 10<8>(exponent) miles
Rationale: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 ×10<12>(exponent) miles
Answer: (D) 587 × 10<12>(exponent) miles
Question: An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 40 miles per hour, then 50 miles per hour, then 60 miles per hour. If the test took 74 hours to complete, how many miles was the car driven during the entire test?
(A) 3600
(B) 3400
(C) 3300
(D) 3500
(E) 3200
Rationale: x is the segment to be traveled
x/40+x/50+x/60 =74
or 74x/1200 =74
x = 1200miles . total distance =3*1200 = 3600 miles
A
Answer: (A) 3600
Question: Two pipes A and B can separately fill a tank in 12 minutes and 16 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 5min
(B) 7min
(C) 8min
(D) 9min
(E) 10min
Rationale: 4/12 + x/16 = 1
x = 10
ANSWER:E
Answer: (E) 10min
Question: Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 60 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
(A) 20
(B) 34
(C) 38
(D) 40
(E) 48
Rationale: Nice question +1
We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 48
Hence answer is E
Answer: (E) 48
Question: There are, in a certain league, 50 teams, and each team face another team for a total of 4 times. How many games are played in the season?
(A) 6660
(B) 3600
(C) 2400
(D) 4900
(E) 5400
Rationale: By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 4900
Option D.
Answer: (D) 4900
Question: Trains A and B start simultaneously from stations 450 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 50 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?
(A)  112
(B)  133
(C)  150
(D)  167
(E)  225
Rationale: Since we know the distance (450) and the combined rate (100), we plug it into the formula:
Distance = Rate * Time
450 = 100 * Time
We can solve for the time they will meet cause we added the rate of Train A and Train B together.
So the time will be 450/100 from dividing 100 on both sides to isolate Time in the equation above.
Time will be 4.5 hours so now you can plug that in for Train A’s distance.
Distance = Rate * Time
Distance = 50 * 4.5
Distance = 225 according to answer choice E.
Answer: (E)  225
Question: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
(A) Rs. 21,000
(B) Rs. 22,500
(C) Rs. 25,300
(D) Rs. 25,800
(E) Rs. 26,800
Rationale: sell at 18700 he got a loss of 15% means, This 18700 is 85% not 100%.
To get 1% : 18700/85=220; Then 220 is 1%.
To get 100% : 220x100=22000.
To get 115% : 220x115=25300
answer :C
Answer: (C) Rs. 25,300
Question: A certain smoothie A is three-fifths blueberries and 40% raspberries by weight. Another smoothie B is three-quarters banana and one-quarter raspberries by weight. If the mixed smoothie of A and B is 30% raspberries by weight, how much weight of this mixture belongs to smoothie A?
(A) 10%
(B) 33.33%
(C) 45%
(D) 50%
(E) 66.66%
Rationale: A is 40% raspberries;
B is 25% raspberries.
A and B is 30% raspberries;
30% raspberries in the mixed smoothie of A and B come from 40% raspberries in A and 25% raspberries in B, thus:
0.3(A+B)=0.4A+0.25B --> 0.1A=0.05B --> A/B=1/2 --> A/(A+B)=1/3.
Answer: B.
Answer: (B) 33.33%
Question: There are 600 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
(A) 100
(B) 200
(C) 250
(D) 300
(E) 400
Rationale: There are 594 managers and 6 others. The 6 others would compose 2% of the total number of people if there were 300 people in the room. Thus 300 managers must leave.
The answer is D.
Answer: (D) 300
Question: For which of the following does f(r)−f(s)=f(r−s) for all values of r and s?
(A) f(a)=a^2
(B) f(a)=a/2
(C) f(a)=a+5
(D) f(a)=2a−1
(E) f(a)=|a|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(r) = r^2 and f(s) = s^2
so L.H.S = r^2 - s^2
and R.H.S = (r-s)^2 ==> r^2 + s^2 -2rs.
so L.H.S not equal to R.H.S
with option 2. f(r) = r/2 and f(s) = s/2
L.H.S = r/2 - s/2 ==> 1/2(r-s)
R.H.S = (r-s)/2
so L.H.S = R.H.S which is the correct answer.
B
Answer: (B) f(a)=a/2
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
(A) 153
(B) 150
(C) 146
(D) 144
(E) 89
Rationale: Let x be the original 2-digit number.
If each digit is halved, then the sum of G and H is 3x/2.
Note the sum must be a multiple of 3 and less than 150.
Of these five choices, only 144 satisfies these two conditions.
The answer is D.
Answer: (D) 144
Question: Two goods trains each 625 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 40
(B) 45
(C) 48
(D) 60
(E) 44
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 625 + 625 = 1250 m.
Required time = 1250 * 6/125 = 60 sec.
Answer: Option D
Answer: (D) 60
Question: What is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other?
(A) 3: 6
(B) 1.5: 1
(C) 3: 1.5
(D) 2: 1
(E) 3: 2
Rationale: d = 1.5d d = d
a√2 = 1.5d a√2 = d
a = 1.5d/√2 a = d/√2 => 1.5: 1
Answer: B
Answer: (B) 1.5: 1
Question: A landlady has been paid $329,864 to her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to confirm that the money has been paid evenly by all 9 of her house rentors?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount the landlady should add to her saving account to ensure that every rentor has paid evenly,
she needs to make the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Answer: (D) $4
Question: A company run by 20 men can produce 1000 pencils in a day. One-fifth of the pencils produced are defective and one-quarter of all pencils produced are rejected by quality control technician. If one-tenth of the nondefective pencils are rejected by mistake, and if all the pencils not rejected are sold, then what percent of the pencils sold by the company are defective?
(A) 4%
(B) 10%
(C) 8%
(D) 6%
(E) 2%
Rationale: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 4 of every 100 that are sold (not rejected) and defective, which implies Answer A.
Answer: (A) 4%