divelab/Sys2Bench huggingface dataset:
Question: ----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 170 students answered yes only for subject M, how many of the students did not answer yes for either subject?
Options:
A)100
B)230
C)300
D)400
E)500
Rationale: Since 170 students answered yes only for subject M, then the remaining 330 students who answered yes for subject M, also answered yes for subject R. So, 330 students answered yes for both subjects.
If 320 students answered yes for both subjects, then 400-330=70 students answered yes only for subject R.
So, we have that:
200 students answered yes only for subject M;
70 students answered yes only for subject R;
300 students answered yes for both subjects;
Therefore 800-(200+70+300)=230 students did not answer yes for either subject.
Answer: B.
Answer: B
Question: If M is a negative integer and Q is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, M, 0, 1, 3, Q, 7}?
I. -1.5
II. -2
III. 0
Options:
A) I only
B) II only
C) III only
D) I and III only
E) None
Rationale: If M is a negative integer and Q is a positive integer,The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either=E
Answer: E
Question: How many of the positive divisors Q of 120 are also multiples of 4 not including 120?
Options:
A)3.
B)4.
C)5.
D)7.
E)8.
Rationale: 4,8,12,20,24,40,60. (7) is the answer
Other way : factors of 120 = 2^3 * 3*5
Separate 2^2 ( which means 4)
Now, calculate the number of other factors.
Q=2*3*5 = total positive factors are 2*2*2 = 8
This 8 factors include 120
So subtract 1 from 8
Ans is 7=D
Answer: D
Question: If x/y = 5 and (4a - x)/(b - y) = 5, then the value of a/b is?
Options:
A) –3
B) -2
C) 1
D) 5/4
E) 3
Rationale: x = 5y
4a - 5y = 5(b - y)
4a - 5y = 5b - 5y
4a = 5b
a/b = 5/4
Answer: D
Answer: D
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 3 hours. Harvesting machine K harvested how many acres of wheat per hour?
Options:
A) 7
B) 8
C) 12
D) 13
E) 17
Rationale: Rate of H = 3 acres/hr
Remaining land to be harvested = 100 - 40 = 60
Rate of H and K = 60/3 = 20 acres/hr
Rate of K = 20-3= 17
Answer: E
Answer: E
Question: On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on November 1 than were in stock on January 1?
Options:
A) 8
B) 12
C) 40
D) 32
E) 36
Rationale: Jan 1 = C
Feb 1 = C - 4
March 1 = C - 8
April 1 = C - 12
May 1 = C - 16
June 1 = C - 20
July 1 = C - 24
Aug 1 = C - 28
Sept 1 = C - 32
Oct 1 = C - 36
Nov 1 = C - 40
Difference between stock on November 1 than were in stock on January 1 will be -
C - ( C - 40 )= 40
Hence answer will be (C)
Answer: C
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Find the sum?
Options:
A)30
B)15
C)40
D)45
E)20
Rationale: a2+b2+c2=138 and(ab+bc+ca)=131
a+b+c^2=400
root(400)=20
ANSWER E
Answer: E
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)227
B)540
C)882
D)266
E)222
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer: D
Answer: D
Question: Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
Options:
A)$506.00
B)$726.24
C)$900.00
D)$920.24
E)$926.24
Rationale: If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.
Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;
Total: 200+306+(~420)=~$926.
Answer: E.
Answer: E
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
Options:
A)120
B)110
C)130
D)140
E)150
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2
Answer: Option A
Answer: A
Question: When 10 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
Options:
A)10
B)24
C)46
D)48
E)45
Rationale: Explanation:
Let the number be x. Then,
x - 10 = 7x/12 => x - 7x/12 = 10
5x/12 = 10 => x = 24
Answer: Option B
Answer: B
Question: 6^4 is equal to which of the following?
Options:
A)1,296
B)752
C)660
D)662
E)1,608
Rationale: A is the correct answer. We do not really need to calculate it. The last digit for 6^4 will be 6. Hence A is the correct answer
Answer: A
Question: In a group of cows and hens, the number of legs are 18 more than twice the number of heads. The number of cows is
Options:
A)5
B)7
C)9
D)12
E)14
Rationale: Explanation:
Let the number of cows be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 18
4x + 2y = 2x + 2y + 18
2x = 18
x = 9.
Answer: C
Answer: C
Question: If a is an even integer and b is an odd integer which of the following must be an odd integer :
Options:
A)a/b
B)ab
C)2a+b
D)2(a+b)
E)3a/b
Rationale: We can always look for low hanging fruits first to solve such questions under 30secs.
Expression in C, is basically 2*Even+Odd or simply Even+Odd which is always going to be odd.
Hence C
Answer: C
Question: Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. Find the larger integer.
Options:
A)8
B)16
C)32
D)48
E)54
Rationale: One option is to set up the equations and solve:
If the ratio of two integers x and y is 1 to 4, then 4x=y, where x is the smaller integer.
If adding 12 to the smaller integer makes the ratio 1 to 1, then x+12=y.
Substituting y=4x into the second equation yields x+12=4x.
So, x=4 (smaller integer) and, y=4x=16 (larger integer) so B is the correct answer.
Another option is to TEST the answer choices.
A) the larger number is 8
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 2
If 12 is added to the smaller number, the ratio becomes 1 to 1
If we add 12 to the smaller number (2), we get 14.
So, the new ratio is 14 to 8 which is the same as 7 to 4.
No good. We want a resulting ratio of 1 to 1
ELIMINATE A
B) the larger number is 16
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 4
If 12 is added to the smaller number, the ratio becomes 1 to 1
If we add 12 to the smaller number (4), we get 16
So, the new ratio is 16 to 16 which is 1 to 1.
Therefore (B) is correct.
C) the larger number is 32
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 8
If 12 is added to the smaller number, the ratio becomes 1 to 1
If we add 12 to the smaller number (8), we get 20
So, the new ratio is 20 to 32 which is 5 to 8.
No good. We want a resulting ratio of 1 to 1
ELIMINATE C
D) the larger number is 48
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 12
If 12 is added to the smaller number, the ratio becomes 1 to 1
If we add 12 to the smaller number (12), we get 24
So, the new ratio is 24 to 48. This is the same as the ratio of 1 to 2
No good. We want a resulting ratio of 1 to 1
ELIMINATE D
E) the larger number is 54
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 13.5 (which is not an integer)
Since both numbers are integers, the larger number cannot be 54.
ELIMINATE E
Therefore B is the only correct choice.
Answer: B
Question: The 38 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
Options:
A)4
B)6
C)8
D)9
E)10
Rationale: The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=38
solving for x you get 10
Answer E
Answer: E
Question: Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 30, find the ages of Toby and Debby?
Options:
A)10 and 14
B)3 and 7
C)6 and 10
D)5 and 10
E)12 and 16
Rationale: Let the age of Debby be x and Toby be x-4
3 ( x + x-4 ) = 30
x = 7
The ages of Toby and Debby are 3 and 7.
Answer : B
Answer: B
Question: A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120.To obtain equal dividends from both,he must invest the money in the ratio :
Options:
A)3 : 4
B)3 : 5
C)4 : 5
D)16 : 15
E)None
Rationale: Solution
For an income of Rs. 1 in 9% stock at 96, investment = Rs. (96/9)= Rs. 32/3 .
For an income of Rs. 1 in 12% stock at 120, investment = Rs.(120/12) = Rs. 10.
∴ Ratio of investments = 32/3 :10 =32:30 = 16:15
Answer D
Answer: D
Question: When asked how old she was, Pooja replied, 'In 2 years I will be twice as old as I was five years ago.'
How old is she ?
Options:
A)11 years
B)12 years
C)8 years
D)10 years
E)15 years
Rationale: B
12 years
Answer: B
Question: Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
Options:
A){9, 11}
B){2, 10}
C){10, 18}
D){7, 13}
E){16, 16}
Rationale: answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is more. therefore accepted
answer is A mean is 10 and S.D decreases minimum.
A
Answer: A
Question: Out of 6 balls a pair is to be selected for a game. At most, how many different pairs are possible?
Options:
A)100
B)90
C)50
D)15
E)25
Rationale: N=6C2=6!/(4!2!)=6*5/2=15
Correct Option: D
Answer: D
Question: A train starts with the speed of 50km/hr with its speed increasing every two hours by 20kmph. In how many hours will it cover 330 kms
Options:
A)4 hrs
B)5 hrs
C)6 hrs
D)4 ½ hrs
E)5 hrs
Rationale: Explanation:
Distance covered in first 2 hours = 50×2 =100km
Distance covered in next 2 hours = 70×2 =140km
Remaining distance = 330 -100-140 =90km
Speed of the fifth hour =90km/hr
Time taken to cover 90km = 90/90 = 1 hr
Total time taken = 2+2+ 1 = 5 hrs
Answer: Option B
Answer: B
Question: A cyclist covers a distance of 500m in 4 min 30sec. What is the speed in km/hr of the cyclist?
Options:
A)2
B)2.5
C)3.2
D)4.6
E)2.8
Rationale: distance = 500 m
time = 4min 10 sec = 250 sec
speed = (500/250) m/s = 2m/s
speed in km/hr = 2*18/5 = 3.2 km/hr
correct option is C
Answer: C
Question: A certain tire company can produce tires at a cost of $22,500 per batch plus $9 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. If a batch of 15,000
tires is produced and sold, what is the company’s profit per tire?
Options:
A)$9.00
B)$9.50
C)$11.00
D)$13.50
E)$20.00
Rationale: CP(15000 tires) = $22500 +($9×15000) =$157500
SP (15000 tires) = $20×15000 = $300000
Profit = SP-CP
= $300000-$157500= $142500
PROFIT/TIRE = $142500/15000 = $9.50
Answer B
Answer: B
Question: During a Thanksgiving weekend, a car rental company rented six-tenths of their vehicles, including three-fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
Options:
A)20%
B)30%
C)40%
D)60%
E)25%
Rationale: 4/10 of all the vehicles were not rented.
(2/5)(3/5) = 6/25 of all the vehicles were 4WDs that were not rented.
(6/25) / (4/10) = 3/5 is the fraction of non-rented vehicles that were 4WDs
1 - 3/5 = 40% of non-rented vehicles were not 4WDs.
The answer is C.
Answer: C
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation s of the mean, what percent of the distribution is less than m+s?
Options:
A) 16%
B) 32%
C) 48%
D) 84%
E) 92%
Rationale: 16%
________________________________________________ m+s
34%
________________________________________________ m
34%
________________________________________________ m-s
16%
since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.
thus 16% lie below m-s and 16% lie above m+s
now below m+s = 16+34+34 = 84%
hence D
Answer: D
Question: Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 5 hours?
Options:
A)675
B)750
C)1,125
D)5,900
E)7,500
Rationale: 8 machines/ 360 cans = 5 machines/ x cans
8x= 1800
x=225
(225)(5 hours)= 1125 cans. The answer is C.
Answer: C
Question: A sum was put a simple interest at a certain rate for 1 years. Had it been put at 6% higher rate, it would have fetched Rs. 30 more. The sum is:
Options:
A)s.500
B)s.600
C)s.700
D)s.800
E)s.900
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x Ã— (R+6) Ã— 1/100âˆ’xÃ—RÃ—1/100=30
â‡’x Ã— 6Ã—1/100=30
â‡’x Ã— 1 /100=5
â‡’x=500
Answer : Option A
Answer: A
Question: If 12 men do a work in 80 days, in how many days will 16 men do it?
Options:
A)20
B)29
C)22
D)60
E)12
Rationale: 12 * 80 = 16 * x
x = 60 days
Answer: D
Answer: D
Question: The greatest common factor of positive integers m and n is 10. What is the greatest common factor of (2m^2, 2n^2)?
Options:
A)2
B)10
C)100
D)200
E)400
Rationale: m = 10j and n = 10k, where the greatest common factor of j and k is 1.
2m^2 = 2*10*10*j^2 and 2n^2 = 2*10*10*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*10*10 = 200
The answer is D.
Answer: D
Question: At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married?
Options:
A)5⁄7
B)7⁄10
C)2/7
D)7⁄30
E)5⁄70
Rationale: --------------------M------W--------Total
Marrried----------20-----20---------40
Not married-----10-----50---------60
Total-------------30-----70--------100
need married woman/total woman, so 20/70=2/7
C
Answer: C
Question: Two cars cover the same distance at the speed of 60 and 62 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Options:
A)1873
B)1848
C)1860
D)1838
E)1939
Rationale: Explanation:
60(x + 1) = 62x
X = 30
60 * 31 = 1860 km
Answer: Option C
Answer: C
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
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: The average of first 10 natural numbers is?
Options:
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
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:
Options:
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
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?
Options:
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
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?
Options:
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
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
Options:
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
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?
Options:
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
Question: When 1/10 percent of 6,000 is subtracted from 1/10 of 6,000, the difference is
Options:
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
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.
Options:
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
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?
Options:
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
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?
Options:
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
Question: What was the day of the week on, 18th July, 1776?
Options:
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
Question: If a2 - b2 = 10 and a*b = 8, find a4 + b4.
Options:
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