divelab/Sys2Bench huggingface dataset:
Question: Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -4 then by what factors will the Mean,Variance and Standard Deviation respectively change ?
Options:
A)-4,-4,-4
B)-4,4,4
C)1,1,1
D)-4,16,4
E)4,4,16
Rationale: Mean: If all values are multiplied by -4 then their sum will also be multiplied by -4 so Mean will also get -4
Variance:
Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values
When we multiply all the values by -4 then the difference between the mean and the individual values also gets multiplied by -4 and the square of that difference becomes 16. So, the variance gets multiplied by a factor of 16
SD:
Standard Deviation is the square root of variance so sqrt(16)=4. So SD gets multiplied by a factor of 4.
So, answer will be D.
Answer: D
Question: If two-third of a bucket is filled in 90 seconds then the time taken to fill the bucket completely will be .
Options:
A)90 seconds
B)70 seconds
C)135 seconds
D)100 seconds
E)120 seconds
Rationale: 2/3 filled in 90 seconds
1/3 filled in 45 seconds
then 2/3+1/3=90 + 45 seconds = 135 seconds
ANSWER: C
Answer: C
Question: Stalin and Heather are 20 miles apart and walk towards each other along the same route. Stalin walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 20 minutes after Stalin, how far from the original destination has Heather walked when the two meet?
Options:
A)4 miles
B)6 miles
C)9 miles
D)10 miles
E)12 mile
Rationale: Original distance between S and H = 20 miles.
Speed of S = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by S = t+20/60 = t+2/6 hours.
Now, the total distances traveled by S and H = 20 miles ---> 6*(t+2/6)+5*t=20 ---> t= 8/11 hours. Thus H has traveled for 8/11 hours giving you a total distance for H = 5*8/11 ~ 4 miles.
A is thus the correct answer.
P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Answer: A
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is?
Options:
A)6 km
B)3 km
C)9 km
D)5 km
E)1 km
Rationale: Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 47/60
47x/60 = 47/60 => x = 1.
Total distance = 3 * 1 = 3 km.
Answer: B
Answer: B
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
Options:
A)200
B)230
C)300
D)350
E)400
Rationale: Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 × (1/8) = 400
E)
Answer: E
Question: A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?
Options:
A)16 m
B)77 m
C)44 m
D)28 m
E)11 m
Rationale: n:
Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer:D
Answer: D
Question: A man goes from A to B at a speed of 60 kmph and comes back to A at a speed of 40 kmph. Find his average speed for the entire journey?
Options:
A)49 kmph
B)58 kmph
C)44 kmph
D)47 kmph
E)48 kmph
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/60) + (d/40]
= (2d)/[5d/120) => 48 kmph.
Answer:E
Answer: E
Question: Find the simple interest on Rs. 72,000 at 16 2/3% per year for 9 months.
Options:
A)7500
B)6500
C)9000
D)9500
E)None of them
Rationale: P = Rs.72000,R = 50/3% p.a and T = 9/12 years = 3/4years.
Simple Interest = (P*R*T)/100 = Rs.(72,000*(50/3)*(3/4)*(1/100))= Rs.9000
Answer is C.
Answer: C
Question: Tim went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)17.13
B)18
C)19.7
D)21.3
E)21.5
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
C)
Answer: C
Question: The width of a rectangular hall is ½ of its length. If the area of the hall is 578 sq.m, what is the difference between its length and breadth?
Options:
A)8m
B)10m
C)12m
D)15m
E)17m
Rationale: Let the length of the hall be x m
Breadth of the hall = 1x/2 m
Area of the hall = Length * Breadth
578 = x * 1x/2
x² = 1156
x =34
Difference between the length and breadth of the hall = x - 1x/2 = x/2
=34/2 = 17m
ANSWER:E
Answer: E
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 12% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1640 in taxes, what is the first tier's price level?
Options:
A)$1600
B)$6000
C)$6050
D)$7050
E)$13000
Rationale: Let T be the tier price, P be total price = 14000
Per the given conditions:
0.12T + 0.08(P-T) = 1640 ----> T= 13000. E is the correct answer.
Answer: E
Question: A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres?
Options:
A)14 minutes
B)12 minutes
C)15 minutes
D)18 minutes
E)None of these
Rationale: Explanation:
As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute
To climb 26 metres, the time required is:
The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes
Also, the last 5 metres it climbs in another 1 minute
Hence, total time required = 14 + 1 = 15 minutes
ANSWER C
Answer: C
Question: A certain league has two divisions. The respective divisions had 11 and 13 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
Options:
A) 41
B) 42
C) 45
D) 47
E) 49
Rationale: Overall, there can be 47 minuses. Tus, it is D.
Answer: D
Question: On a wedding catering service, An experienced chef can prepare a service for a wedding in 10 hours while an novice chef would finish the preparations in 18 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: Experienced chefs work = 1 wedding/10 hours
Novice chefs work = 1 wedding/18 hours
Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equalx
1hr and 36mins = 8/5 an hour
x/10 + x/18 = 1 wedding / (8/5)
x/10 + x/18 = 5/8
x=4
So there are 4 novice chefs and 4 experienced chefs. In total there are 8. The answer is E.
Answer: E
Question: A rectangular swimming pool is 20 feet by 22 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 728 square feet. What is the width of the deck?
Options:
A)2
B)4
C)3
D)5
E)6
Rationale: Let the width =W
Total Area of the pool and deck= (2W+20)(2W+22)
We can Test the answer choices along with unit digit method
A) 2 feet ...........24*26 has unit digit 8..........Eliminate
B) 2.5 feet.........25*33 has unit digit 5..........Eliminate
C) 3 feet............26*28 has unit digit 4...........Hold
D) 4 feet............28*30 has unit digit 0...........Eliminate
E) 5 feet............30*32 has unit digit 0...........Eliminate
Answer: C w=3
Answer: C
Question: The value of a machine depreciates at 21% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
Options:
A)$257615
B)$437615
C)$127615
D)$117615
E)$157615
Rationale: The value of the machine after two years = 0.79 * 0.79 * 1,50,000 = $96,000
SP such that a profit of $24,000 is made = 93,615 + 24,000 = $1,17,615
D
Answer: D
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1568?
Options:
A)1000
B)2777
C)2889
D)1400
E)2771
Rationale: 1568 = P [1 + (5*12/5)/100]
P= 1400.Answer:D
Answer: D
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum y of all the even integers between 99 and 301?
Options:
A)10,100
B)20,200
C)22,650
D)40,200
E)45,150
Rationale: I would solve it in a different way.
First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101
Average = (301+99)/2 = 400/2 = 200
Sum y= Average*total count = 200*101 = 20,200
Answer is B
Answer: B
Question: John went to the Hospital at the speed of 60 km per hour while returning for his home he covered the half of the distance at the speed of 10 per hour, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest 1/2 of the distance at the speed of 30km per hour. The average speed of the John in the whole length of journey is?
Options:
A)20 km/hr
B)22 km/hr
C)24 km/hr
D)26 km/hr
E)30 km/hr
Rationale: Let distance between his home and hospital =
d
d km
Total distance travelled
=
d
+
d
=
2
d
=d+d=2d km
Total time taken
=
d
60
+
(
d
2
)
10
+
(
d
2
)
30
=d60+(d2)10+(d2)30
=
d
60
+
d
20
+
d
60
=
5
d
60
=
d
12
=d60+d20+d60=5d60=d12 hr
Average speed in the whole journey
=
2
d
(
d
12
)
=
2
d
×
12
d
=
24
=2d(d12)=2d×12d=24 km/hr
C
Answer: C
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options:
A)22887
B)2778
C)2797
D)8112
E)1712
Rationale: Explanation:
A = 7500(26/25)2 = 8112
Answer:D
Answer: D
Question: Martha has the unique talent of being able to guess other people’s height and weight. For every four people that Martha meets, she consistently guesses the people’s correct height three times, and for every six people that she meets, she consistently guesses the people’s correct weight four times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?
Options:
A)8/27
B)7/8
C)49/81
D)98/125
E)125/144
Rationale: Probability that she guesses the height correctly P(h)=3/4
Probability that she guesses the weight correctlyP(w)=4/6
Probability that she guesses both weight and height correctly(P(h)*P(w))=3/4 * 4/6= 12/24
Now the Q asks about the probability of this happening atleast once.
We calculate it by finding the probability of not being able to guess in any of the three occasions.
Probability of not being able to guess any no. of times =1-12/24=12/24=1/2
For all three occasions P(A)=1/2 * 1/2 * 1/2=1/8
Probability of the event happening atleast once=1- P(A)=1-1/8=7/8
Ans should be B
Answer: B
Question: Express a speed of 46 kmph in meters per second?
Options:
A)10.78 mps
B)12.78 mps
C)97.78 mps
D)17.78 mps
E)18.78 mps
Rationale: 46 * 5/18
= 12.78 mps
Answer: B
Answer: B
Question: From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn.
Options:
A)4/13
B)1/52
C)1/4
D)1/3
E)None of these
Rationale: Explanation:
Total number of cases = 52
Total face cards = 16 [favourable cases]
So probability = 16/52 = 4/13
Option A
Answer: A
Question: David bought a 1-year, $5,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Options:
A)$310
B)$425
C)$450
D)$300
E)$312.50
Rationale: 10 percent compounded semiannually --> 5% in 6 moths.
For the first 6 moths interest was 5% of $5,000, so $250;
For the next 6 moths interest was 5% of $5,250, so $262.50
Total interest for 1 year was $250+$262.50=$312.50
Answer : E
Answer: E
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ?
Options:
A)2015
B)2088
C)270
D)1881
E)1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2014) = 2015
Ans: A
Answer: A
Question: With # andeach representing different digits in the problem below, the difference between #and ## is 712. What is the value of?
#
-##
____
712
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: 100x
-(10x +x)
-----------
89 x= 712
x = 8
B
Answer: B
Question: A man walking at a rate of 10km/hr crosses a bridge in 15 minutes. The length of the bridge is?
Options:
A)1521
B)1492
C)1667
D)2500
E)1112
Rationale: Speed = 10*5/18 = 50/18 m/sec
Distance covered in 15 minutes = 50/18 *15 *60 = 2500 m
Answer is D
Answer: D
Question: A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)500
B)289
C)350
D)882
E)281
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 48 = 50/3
3(x + 300) = 2400 è x = 500m.
Answer: A
Answer: A
Question: A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 135 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?
Options:
A)8%
B)9%
C)11%
D)12.5%
E)14.8%
Rationale: Typical dosage is Dose : weight :: 2: 15.
Now if weight is 135 (Multiplying factor is 9: (135/15)) then typical dosage would be 2 *9 = 18cc.
Dosage = 18 cc. Dosage is greater by 2 cc.
% dosage is greater: (2 / 18)*100 = 11.11 %
C is the answer.
Answer: C
Question: If x is an integer such that 3 < x < 10, 5 < x < 18, 9 > x > –2, 8 > x > 0, and x + 1 < 9, then x is
Options:
A)3
B)5
C)7
D)9
E)11
Rationale: 3 < x < 10,
6 < x < 18,
-2 < x <9
0 < x < 8
x<8
From above: 6< x < 8 --> x = 7.
Answer: C.
Answer: C
Question: In an election between two candidates, the winner has a margin of 20% of the votes polled. If 1000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election?
Options:
A)10000
B)5000
C)15000
D)20000
E)6000
Rationale: Winner - Looser
60% - 40%
If 1000 people change their mind and vote for the loser:
Winner - Looser
40% - 60%
Thus 1,000 people compose 20% of all voters, which means that the total number of votes is 5,000.
Answer: B
Answer: B
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)287 cm2
B)785 cm2
C)285 cm2
D)785 cm2
E)295 cm2
Rationale: Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
Answer: Option C
Answer: C
Question: A summer camp has 150 children coming for the summer. Out of them, 60% have applied for the water sports programme and 80% have applied for rock climbing. How many campers have applied for both?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: The total number of campers coming for the summer is n = 150.
The number of campers who have applied for the water sports activities is 60% of it, thus
n (A)=60/100×150=6×15=90
The number of campers who have applied for rock climbing is 80%, thus
n (B)=80/100×150=8×15=120.
In order to calculate the number of campers who have applied for both programs we can use the following equation:
n (AnB)=n (A)+n (B) -n =90+120-150=50=60.
So, 60 campers have applied for both water sports and rock climbing.
ANSWER: B
Answer: B
Question: Three workers have a productivity ratio of 3 to 5 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 8th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
Options:
A)12 to 1
B)6 to 1
C)5 to 1
D)20 to 7
E)1 to 5
Rationale: The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job;
The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 3*7=21
The ratio thus is 60 to 21, or 20 to 7.
Answer: D.
Answer: D
Question: Convert the 9/36 m/s into kilometers per hour?
Options:
A)0.9 kmph
B)9.9 kmph
C)1.3 kmph
D)1.2 kmph
E)5.7 kmph
Rationale: 9/36 m/s = 9/36 * 18/5 = 9/10
= 0.9 kmph.
Answer: A
Answer: A
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 110 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10
B)25
C)77
D)55
E)22
Rationale: Speed of the boat in still water = (60+110)/2 = 85 kmph. Speed of the stream
= (110-60)/2
= 25 kmph.
Answer: B
Answer: B
Question: The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
Options:
A)187.89 cm
B)180.29 cm
C)123.98 cm
D)149.98 cm
E)146.89 cm
Rationale: Calculated average height of 35 boys = 182 cm.
Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182 cm - (166 cm - 106 cm)/35
= 182 cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm
= 182 cm - 1.71 cm = 180.29 cm.
Answer: B
Answer: B
Question: John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him?
Options:
A)10
B)67
C)32
D)44
E)55
Rationale: 75-20=55. Answer is E
Answer: E
Question: Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
7 ~ 2 ~ 7 ~ 4 = ____
Options:
A)3538
B)2418
C)2873
D)3258
E)4268
Rationale: B
The rule that is being followed here is
P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]
Using the same rule in the incomplete equation,
7 ~ 2 ~ 7 ~ 4 = [first digit of (7 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (7 * 4)]
= 2418
Thus 2418 is the missing number.
Answer: B
Question: The speed at which a man can row a boat in still water is 9.5 kmph. If he rows downstream, where the speed of current is 8.5 kmph, what time will he take to cover 45.5 metres?
Options:
A)18 seconds
B)8.4seconds
C)5 seconds
D)9.1 seconds
E)9.5econds
Rationale: Speed of the boat downstream = 9.5 +8.5
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 45.5 m = 45.5/5
= 9.1 seconds.
Answer:D
Answer: D
Question: If x is 20 percent more than y and y is 30 percent less than z, then x is what percent of z?
Options:
A)500%
B)250%
C)500/3%
D)84%
E)60%
Rationale: Z = 100 ; Y = 70 so X = 84
X as % of Z = 84/100 * 100 => 84%
Answer will be (D)
Answer: D
Question: Tommer spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommer won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
Options:
A)330
B)500
C)520
D)540
E)620
Rationale: I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, tommer earned$520. Answer choice C.
Answer: C
Question: Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-7) = 0, then f(x) crosses the y-axis at what y-coordinate?
Options:
A)-7
B)-1
C)0
D)1
E)7
Rationale: When x = 1 and when x = -7, the expression f(x) = x² + bx + c equals 0.
Then f(x) = (x-1)(x+7)
f(0) = -7
The answer is A.
Answer: A
Question: In 2000 there were 10000 women stockbrokers in the United States. By 2005 the number had increased to 20000. Approximately what was the percent increase?
Options:
A)1%
B)2%
C)1.5%
D)3%
E)4%
Rationale: The percent increase is (20000-10000)/10000=10000/10000=1%
So the approximate answer is A
Answer: A
Question: At present the son's age is same as was his father's age at the time of his birth. If father's age is 48. Find the son's age after 4 years from now.
Options:
A)30 years
B)24 years
C)28 years
D)29 years
E)38 years
Rationale: Let x be the son's age
And y be the father's age
Then, y=48.
And, x=y-x
==> 2x=y
==> x=y/2
So, x=48/2
x=24.
Son's age after four years,
x+4 = 24+4
= 28 years.
ANSWER:C
Answer: C
Question: A train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?
Options:
A)5
B)12
C)7
D)9
E)5
Rationale: Speed of train relative to man = 60 + 4 = 64 km/hr.
= 64 * 5/18 = 160/9 m/sec.
Time taken to pass the men = 220 * 9/160 = 12 sec.Answer: B
Answer: B
Question: If 2x=4y=z, what is x-y, in terms of z?
Options:
A)z/4
B)z/2
C)z
D)2z
E)4z
Rationale: 2x=4y=z
i.e. x = z/2
and y = z/4
x-y = z/2 - z/4 = z/4
Answer: Option A
Answer: A
Question: The population of cities A and B is equal. The population of city A increases in two successive years by 20% and 15% respectively and that of city B increases successively by 20% and 10% respectively. If the difference in the population of two cities after 2 years is 768, then what was the total population of the two cities initially?
Options:
A)12,800
B)26,500
C)24,600
D)25,600
E)27,600
Rationale: Population of city A = Population of city B = A
M . F of A = 120/100*115/100 = 138/100
M . F of B = 120/100*110/100 =132/100
Population of A after 2 years = A*138/100
Population of B after 2 years = A*132/100
Difference = A/100( 138 –132 ) = 768
A = 768*100/6 = 12800
Total initial population = 12800+12800 = 25,600
ANSWER:D
Answer: D
Question: A man deposits $1000 in a bank at 2% per annum and $ 1500 in UTI at 7% per annum. Find the rate of interest for the whole sum.
Options:
A)5%
B)8%
C)3%
D)7%
E)1%
Rationale: Following the above formula,we have the rate of interest for the whole sum
=(1000*2)+(1500*7)/1000+1500=12500/2500=5%.
Answer is A
Answer: A
Question: Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 4
II. 12
III. 24
Options:
A)I, II, and III
B)I and II only
C)II and III only
D)I and III only
E)II only
Rationale: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Answer: A
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Options:
A)33 1/9%
B)73 1/3%
C)33 1/3%
D)33 1/9%
E)39 1/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: C