divelab/Sys2Bench huggingface dataset:
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
Options:
A)9:1
B)4:7
C)7:1
D)2:5
E)1:6
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
ANSWER:A
Answer: A
Question: John bought a total of 24 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 24 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?
Options:
A)4
B)5
C)6
D)7
E)14
Rationale: Let number of mangoes be x, number of oranges be 24-x
0.80x +(24-x)0.60/24 = 0.65
solving for x, we get x = 6 --> Mangoes 6, Oranges 18
Now, number of oranges to be returned be y
0.80*6 + (18-y)*0.60/24-y = 0.72
solving for y, y = 14
Ans: E
Answer: E
Question: A tank contains 9,000 gallons of a solution that is 6 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Options:
A) 6%
B) 7%
C) 8%
D) 9%
E) 10%
Rationale: We start with 9,000 gallons of a solution that is 6% sodium chloride by volume. This means that there are 0.06 x 9,000 = 54 gallons of sodium chloride.
When 3,000 gallons of water evaporate we are left with 6,000 gallons of solution. From here we can determine what percent of the 6,000 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(540/6,000) x 100 = ?
9/100 x 100 = ?
= 9%
Answer is D.
Answer: D
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by A are?
Options:
A)11
B)18
C)13
D)17
E)12
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
4/25 * 75 = 12
Answer:E
Answer: E
Question: Rs 3600 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.
Options:
A)s 4000
B)s 2800
C)s 1800
D)s 3500
E)s 3100
Rationale: Explanation :
Average rate = (144/3600)*100 = 4
Ratio = 1:1
So, first part = (1/2)*3600 = Rs 1800.
Answer : C
Answer: C
Question: Alex takes a loan of $8,000 to buy a used truck at the rate of 6 % simple Interest.Calculate the annual interest to be paid for the loan amount.
Options:
A)480
B)520
C)460
D)400
E)520
Rationale: From the details given in the problem Principle = P = $8,000 and R = 6% or 0.06 expressed as a decimal.
As the annual Interest is to be calculated, the time period T =1.
Plugging these values in the simple Interest formula,
I = P x T x R
= 8,000 x 1 x 0.06
= 480.00
Annual Interest to be paid = $480
answer :A
Answer: A
Question: On a track for remote controlled racing cars, racing car A completes the track in 57 seconds, while racing car B completes it in 35 seconds. If they both start at the same time after how many seconds will they be side by side again.
Options:
A)275
B)325
C)1995
D)425
E)None of these
Rationale: Time required in seconds will be LCM ( 35, 57 ) = 1995
Hence, answer will be (C) 1995
Answer: C
Question: A train covers a distance of 54 km in 15 min. If it takes 8 sec to pass a telegraph post, then the length of the train is?
Options:
A)470
B)480
C)490
D)500
E)510
Rationale: Speed = (54/15 * 60) km/hr = (216 * 5/18) m/sec = 60 m/sec.
Length of the train = 60 * 8 = 480 m.
Answer: Option B
Answer: B
Question: Four friends built a colony for themselves. They built their own houses at different distances from each other.
Chris lived 60 km away from Alex.
Darren lived 40 km away from Bill.
Chris lived 10 km nearer to Darren than he lived to Bill.
Can you find out how far was Darren's house from Alex?
Options:
A)75 km
B)60 km
C)45 km
D)50 km
E)85 km
Rationale: A
75 km
Explanation:
Distance between Bill and Darren = 40 km
Distance between Bill and Chris + Distance between Chris and Darren = 40 km
Distance between Bill and Chris + (Distance between Bill and Chris - 10) = 40 km
2 * Distance between Bill and Chris = 50 km
Distance between Bill and Chris = 25
Distance between Chris and Darren = 15 km
Therefore, distance between Darren's house and Alex's house = 60 + 15 = 75 km.
Answer: A
Question: Today is Monday. After 61 days, it will be:
Options:
A)SUNDAY
B)SATURSDAY
C)FRIDAY
D)THURSDAY
E)MONDAY
Rationale: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer: Option B
Answer: B
Question: Graph G has a line of symmetry of x = –5. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?
Options:
A) –8
B) –7
C) –5
D) –4
E) -13
Rationale: Line of symmetry is X=-5; one point is (3,3)
Right side distance =5+3(distance from origin) = 8; therefore Left side distance should be same from line of symmetry =8;
therefore left side co-ordinate=8+5(distance from origin) = 13; as the X coordinate is in 2nd quadrant hence -13
Therefore answer is E
Answer: E
Question: Which of the numbers below is the odd one out
1,5,13,17,25,41,61.
Options:
A)17
B)13
C)5
D)25
E)61
Rationale: 17 is the odd man.. diff between sucessive no.s are multiples of 4
ANSWER:A
Answer: A
Question: Today Roseline, who is 50 years old, and her daughter, who is 20 years old, celebrate their birthdays. How many years will pass before Roseline’s age is twice her daughter’s age?
Options:
A)12
B)13
C)10
D)15
E)18
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
After x years passes Roseline’s age will be (50+x) years old, and her daughter’s age will be (20+x) years old. Since the Roseline’s age is twice her daughter’s age (50+x)= 2 * (20+x) ---> 50+x=40+2x ---> x= 10
The answer is (C).
Answer: C
Question: A photo-mat shop charges $0.55 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $52.52 if each film contains 36 photos?
Options:
A)4 films and 10 photos
B)5 films and 6 photos
C)5 films and 14 photos
D)6 films and 4 photos
E)6 films and 28 photos
Rationale: 1st photo = 0.55
Subsequent = 0.55*0.6=0.33
Price of 1 full film=0.55+0.33*35=12.1
Price of 4 full film = 12.1*4=48.4
52.52-48.4=4.18
4.18=0.55+0.33x
x=11
52.58--->4 full films and 1+11=12 photos
Answer: A
Answer: A
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 7
Options:
A)1/2
B)7/12
C)5/13
D)5/12
E)6/17
Rationale: Total number of cases = 6*6 = 36
Favourable cases = [(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,4),(5,6),(5,3),(5,5),(6,2),(6,3),(6,4),(6,5),(6,6)] = 15
So Probability = 15/36 = 5/12
Answer is D
Answer: D
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)Rs. 1090
B)Rs. 1160
C)Rs. 1190
D)Rs. 1202
E)Rs. 1204
Rationale: since,c.p=1400
loss%=(c.p-s.p)/c.p*100
15=(1400-s.p)/1400*100
so,after solving answer=1190.
ANSWER:C
Answer: C
Question: total dinning bill of 8 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
Options:
A)11.84
B)12.84
C)23.84
D)19.11
E)10.12
Rationale: dinner bill of 8 person = 139 + 10% tip
so,
10% of 139 = (139*10)/100 = 13.9
So, the actual total amount = 139+13.9 = $ 152.9
so per head bill = 152.9/8 = $ 19.11
ANSWER:D
Answer: D
Question: The number of arrangements that can be made with the letters of the word JOHNNIE so that the vowels occupy the even places?
Options:
A)A)122
B)B)134
C)C)144
D)D)156
E)E)176
Rationale: Explanation:
The word JOHNNIE has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
C
Answer: C
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 8?
Options:
A)1
B)3
C)5
D)4
E)6
Rationale: You should consider the worst case scenario: if you pick numbers 0, 1, 2,3 and 4 then no two numbers out of these 5 add up to 8.
Now, the next, 6th number whatever it'll be (5,6,7,8 or 9) will guarantee that two number WILL add up to 8. So, 6 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 8
Answer: E
Answer: E
Question: In what proportion must wheat at Rs. 15 per kg. be mixed with wheat at Rs. 18 per kg. So that the mixture will be worth Rs. 17 per kg. ?
Options:
A)1 : 9
B)1 : 3
C)1 : 2
D)1 : 1
E)1 : 8
Rationale: Explanation:
Wheat/Rs. 15 per kg.
Wheat/Rs. 18 per kg.
For the mixture to be worth Rs. 17 per kg. The ratio should be:
(18 – 17) : (17 – 15)
1 : 2
ANSWER:C
Answer: C
Question: What is the remainder of R=3^19 when divided by 10?
Options:
A)0
B)1
C)5
D)7
E)9
Rationale: I looked for patterns:
^2 - units digit 9
^3 - units digit 7
^4 - units digit 1
^5 - units digit 3
hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9
and we can then see:
^16 - units digit 1, or
^18 - units digit 9
and ^19 - units digit 7
therefore, R=when divided by 10, the remainder must be 7.D
Answer: D
Question: In Set T, the average (arithmetic mean) equals the median R. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.
Options:
A)I only
B)I and II
C)II and III
D)I, II, and III
E)IV only
Rationale: This is a very good 'trap question'.
Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3
If you think that only in 'consecutive integers' the average is equal to the median R you might fall for 'D'.
Ans: E
Answer: E
Question: How many cubes of 3cm edge can be cut out of a cube of 18cm edge
Options:
A)36
B)232
C)216
D)484
E)None of these
Rationale: Explanation:
number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216
Answer: C
Answer: C
Question: 20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 10:40 in the morning?
Options:
A)32.
B)36.
C)42.
D)46.
E)60.
Rationale: @ 6:30 - 2
@ 7 - 4+7 =11
@ 7:30 - 2
@ 8 - 12
@ 8:30 - 2
@ 9 - 13
@ 9:30 - 2
@ 10 - 14
@10:30 - 2
totals to E=60
Answer: E
Question: Currently guavas cost 60 cents/pound. Due to a disease affecting the guava trees it is expected that next month apples will cost 250% more than they do currently. How much are guavas expected to cost next month?
Options:
A)110 cents /pound
B)150 cents /pound
C)180 cents /pound
D)200 cents /pound
E)210 cents /pound
Rationale: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 60 cents/pound + (250/100)(60 cents/pound)
= 60 cents/pound + 150 cents/pound
= 210 cents /pound
Answer : E
Answer: E
Question: A division of a company consists of four men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
Options:
A)2/9
B)3/11
C)4/15
D)5/18
E)6/25
Rationale: Total number of ways to select 2 members = 9C2 = 36
Total number of ways to select 2 females = 5C2 = 10
P(two females) = 10/36 = 5/18
The answer is D.
Answer: D
Question: 8+8
Options:
A)5
B)17
C)16
D)23
E)19
Rationale: C
Answer: C
Question: Which of the following is/are terminating decimal(s)?
I 299/(32^123)
II 189/(49^99)
III 127/(25^37)
Options:
A)I only
B)I and III
C)II and III
D)II only
E)I, II, III
Rationale: The fraction will have terminating decimal if and only if the denominator of the fraction is of the form (2^n)(5^m).
If you look at the denominators:
1) (32^123) => (2^(5*123))(5^0) => Terminating Decimal
2) (49^99) => Can't be expressed as (2^n)(5^m) => Non terminating Decimal
3) (25^37) => (2^0)(5^(2*37)) => Terminating Decimal
Hence 1 and 3 are terminating decimals => Choice [B]
Answer: B
Question: Which of the following can be a perimeter w of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
Options:
A)I only
B)III only
C)II and III only
D)I, II, and III
E)Not I, II, or III
Rationale: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: w>0.
Answer is D.
Answer: D
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)22
B)30
C)48
D)99
E)12
Rationale: Relative speed = 90 + 30 = 120 km/hr.
120 * 5/18 = 100/3 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 3/100 = 30 sec.
Answer: B
Answer: B
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
Options:
A)6:8
B)6:4
C)6:2
D)6:5
E)6:2
Rationale: 5M + 12B ----- 4 days
7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
Answer: D
Answer: D
Question: What percent of a day is seven hours?
Options:
A)20.83%
B)16x1/2%
C)29.16%
D)22x1/2%
E)None of these
Rationale: Explanation :
Required percentage = (7/24100)%
= 29.16%.
Answer : C
Answer: C
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 10 minutes, what part of the cistern will be emptied?
Options:
A)4/9
B)4/3
C)4/2
D)5/9
E)4/1
Rationale: 2/3 ---- 12
? ----- 10 ==> 5/9
Answer: D
Answer: D
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Options:
A)299
B)375
C)27878
D)288
E)212
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375.Answer: B
Answer: B
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 9/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Options:
A)7/17
B)14/31
C)7/15
D)17/35
E)9/19
Rationale: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 9/5 units. Total time for Basic would be 10*1=10 and total time for Deluxe would be 5*9/5=9 --> total time for both of them would be 10+9=19 --> deluxe/total=9/19.
Answer: E.
Answer: E
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned?
Options:
A)Rs.19,828.89
B)Rs.19,828.80
C)Rs.19,828.92
D)Rs.19,822.00
E)Rs.19,828.24
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2
= (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08
= 17000 Principal + Interest = Rs. 19828.80
Answer:B
Answer: B
Question: if 20% of a number is added to second no.,then it increase by 50%.calculate the ratio of these no.
Options:
A)3:2
B)2:3
C)5:2
D)can't be calculated
E)none of these
Rationale: Answer:	let no. be A and B.
(20%of A)+B=150% of B
A/5=3B/2-B=B/2;A/B=5/2,
A:B=5:2
answer C
Answer: C
Question: A and B starts a business with Rs.8000 each, and after 6 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Options:
A)3:2
B)12:5
C)18:10
D)18:14
E)14:11
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 6 months and then withdraws Rs.4000. So, the investment of B for remaining 12 months is Rs.4000 only.
A : B
8000*18 : (8000*6) + (4000*12)
14400 : 96000
A:B = 3:2
Answer: A
Answer: A
Question: 8 x 1.6 - 3 x 1.4/1.3 = ?
Options:
A)21.5
B)22
C)15.8
D)12.8
E)25
Rationale: Given Expression
= (12.8 -4.2)/0.4
= 8.6/0.4
= 8.6/0.4
= 21.5
Answer is A.
Answer: A
Question: What is his percentage profit made by Nancy if she purchased 15 dozen pencils at Rs. 20 per dozen. He sold 8 dozens at 12% profit and the remaining 7 dozens with 15% profit?
Options:
A)10.08%
B)18.08%
C)15.08%
D)12.08%
E)16.08%
Rationale: Explanation :
C.P of 15 dozen = Rs.(20 x 15) = Rs.300
C.P of 8 dozen = Rs. (20 x8) = Rs. 160.
C.P of 7 dozen =Rs. (20 x7) = Rs. 140
profit on 8 dozen at 12% = 12/100*160 = 19.2
profit on 7 remaining dozen at 15% = 15/100*140 = 21
total profit = 19.2 + 21 = 40.2
% profit = ?/100*250 = 40.2
= 16.08%
Answer : E
Answer: E
Question: Two employees M and N are paid a total of $616 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
Options:
A)$270
B)$280
C)$290
D)$300
E)$310
Rationale: 1.2N + N = 616
2.2N = 616
N = 280
The answer is B.
Answer: B
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
Options:
A)338
B)279
C)125
D)776
E)988
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
Answer:C
Answer: C
Question: If (4x + 7)(x + 2) = 8x^2 + x, what is a possible value of x?
Options:
A) 12
B) -7
C) 7
D) -1
E) -14
Rationale: Rearranging the given expression:
(4x + 7)(x + 2) = 8x^2 + x
i.e. 8x^2 + 15x + 14 = 8x^2 + x
i.e. 14x = -14
i.e. x = -14/14 = -1
Answer: Option D
Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible
Answer: D
Question: If a and b are positive integers, and a=3b+12, the greatest common divisor of a and b CANNOT be
Options:
A)1
B)3
C)2
D)5
E)4
Rationale: If b is 1, 2, 3, or 4, then GCD of a and b is 1, 2, 3, and 4 respectively. So, by POE the answer must be D.
Still: if b is a multiple of 5, then a is 12 greater than a multiple of 5, so not a multiple of 5, so both of them cannot be divisive by 5.
Answer: D.
Answer: D
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,00,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 40,000
B)Rs. 50,000
C)Rs. 60,000
D)Rs. 90,000
E)None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (100000 – x) respectively. Then,
1/3x=1/2(100000-x)
=> x/3 + x/2 = 50000
=> 5x/6 = 50000
=> x= 50000 x 6 /5= 60000
Savings in Public Provident Fund = Rs. (100000 – 60000) = Rs. 40000
Answer A
Answer: A
Question: John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, 5, or 6 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?
Options:
A)1/3
B)2/5
C)3/5
D)4/25
E)6/25
Rationale: John will run farther if he runs at 6 mph and Amanda runs at 5 mph, 4 mph, or 3 mph.
In this case, P(John runs farther) = 1/5 * 3/5 = 3/25
John will run farther if he runs at 5 mph and Amanda runs at 4 mph or 3 mph.
In this case, P(John runs farther) = 1/5 * 2/5 = 2/25
John will run farther if he runs at 4 mph and Amanda runs at 3 mph.
In this case, P(John runs farther) = 1/5 * 1/5 = 1/25
Overall, P(John runs farther) = 3/25 + 2/25 + 1/25 = 6/25
The answer is E.
Answer: E
Question: Calculate the sum of first 19 natural numbers.
Options:
A)190
B)120
C)150
D)199
E)110
Rationale: Solution
We know that(1+2+3+.....+19)	= n(n+1)/2
Therefore (1+2+3+....+19)	=(19×20 / 2)
= 190.
Answer A
Answer: A
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 60 per cent. The two reductions together are equal to a single reduction of
Options:
A)45%
B)70%
C)35%
D)32.5%
E)30%
Rationale: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 60percent is reduced which means the new price is merely 40percent of 3/4P
==> (3/4)x(2/5)P = 6/20P is the new price after both deduction which is 30percent of the original value P. This implies this entire series of deduction is worth having discounted 70% of P. So answer is B = 70%
Answer: B
Question: A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $96, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
Options:
A)81
B)84
C)85
D)88
E)90
Rationale: LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =96 OR 1/7T + 1T =96 THEREFORE T= 96*7/8 = 84
B
Answer: B
Question: The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof?
Options:
A)38.
B)40.
C)42.
D)44.
E)45.
Rationale: Let the width= x
x*4x=900
x^2= 225
x= 15
Length= 4*15= 60
difference= 60-15= 45
E is the answer
Answer: E
Question: 5/8th of a job is completed in 10 days. If a person works at the same pace, how many days will he take to complete the job?
Options:
A)8
B)9
C)6
D)2
E)1
Rationale: Explanation:
Solution: It is given that 5/8th of the work is completed in 10 days.
=> Remaining work = 3/8th of total
Applying unitary method:
Total work will be completed in 10 * 8 / 5 days
=> It takes 16 days to complete total work
=> Hence, remaining work days = 16 - 10 = 6 days
ANSWER:C
Answer: C
Question: Which is the least number that must be subtracted from 1828 so that the remainder when divided by 8, 12, 16 is 4?
Options:
A)0
B)4
C)8
D)6
E)2
Rationale: First we need to figure out what numbers are exactly divisible by 8,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(8,12,16) = 48 = 48
number is to be subtracted is 0
The largest such number less than or equal to 1828 is 48*38+4
A
Answer: A
Question: Find the quadratic equations whose roots are the reciprocals of the roots of 2x2 + 5y + 3 = 0?
Options:
A)+ 5y - 2 = 0
B)+ 5y + 2 = 0
C)- 5y + 2 = 0
D)- 5y - 2 = 0
E)of these
Rationale: The quadratic equation whose roots are reciprocal of 2x2 + 5y + 3 = 0 can be obtained by replacing y by 1/y.
Hence, 2(1/y)2 + 5(1/y) + 3 = 0
=> 3x2 + 5y + 2 = 0
ANSWER:B
Answer: B