divelab/Sys2Bench huggingface dataset:
Question: 3 men and 10 boys finish a job in 9 days, 7 men and 7 boys finish it in 8 days. 9 men and 9 boys shall finish it in how many days?
Options:
A)18
B)09
C)07
D)19
E)12
Rationale: 3 M + 10 B ----- 09 days
7 M + 7 B ------- 8 days
9 M + 9 B -------?
21 M + 70 B = 63 M +63 B
7 B= 42 M => 6 M = 1 B =>1 B =6 M
3 M + 60 M = 63 M ---- 9 days
9 M + 54 M = 63 M -----? => 9 days
Answer: B
Answer: B
Question: A man can row his boat with the stream at 16 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)3 kmph
C)6 kmph
D)7 kmph
E)5 kmph
Rationale: DS = 16
US = 4
S = ?
S = (16 - 4)/2 = 6 kmph
Answer: C
Answer: C
Question: Sam's dad is 4 times older than his son. In 22 years from now, however, he'll only be twice his son's age. How old will Sam be 22 years from now?
Options:
A)22 years
B)33 years
C)44 years
D)55 years
E)66 years
Rationale: At the present,
Sam's age is x.
Sam's father's age is y= 4x.
In 22 years from now,
Sam's age will be x+22.
Sam's father's age will be y+22=2 (x+22).
If we take both equations,
y=4x, and
y+22=2 (x+22),
then
y+22=4x+22=2 (x+22)
4x+22=2x+44
4x-2x=44-22
2x=22
x=11
This is, however, Sam's current age. Since the question is how old he'll be in 22 years from now, the answer 11+22=33.
ANSWER: B
Answer: B
Question: A(4, w^2) is the (x, y) coordinate of point located on the parabola Y = X^2 + 9. What is the value of w?
Options:
A)3.
B)4.
C)5.
D)6.
E)9.
Rationale: y=x^2 +9
w^2=4^2+9
w^2=25
W=5
Answer C
Answer: C
Question: Arun, Kamal and Vinay invested Rs.8000, Rs.4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?
Options:
A)10000 and 15000
B)15000 and 10000
C)5000 and 20000
D)20000 and 5000
E)1000 and 15000
Rationale: As both A and B invest the same amounts, the ratio of their profits at the end of the year is equal to the ratio of the time periods for which they have invested.
Thus, the required ratio of their profits = A : B = 8 : 12 = 2 : 3.
Hence, share of A in the total profit = 2/5x25000 = Rs.10000
Similarly, share of B in the total profit =3/5x25000 = Rs.15000 answer :A
Answer: A
Question: If eight persons sit in a row, then the probability that three particular persons are always together is?
Options:
A)1/5
B)1/4
C)1/9
D)1/28
E)3/28
Rationale: Eight persons can be arranged in a row in 8! ways.
Treat the three persons to sit together as one unit then there six persons and they can be arranged in 6! ways.
Again three persons can be arranged among them selves in 3! ways.
Favourable outcomes = 3!6!
Required probability = 3!6!/8! = 3/28
Answer:E
Answer: E
Question: If a(a + 6) = 7 and b(b + 6) = 7, where a ≠ b, then a + b =
Options:
A) −48
B) −6
C) 2
D) 46
E) 48
Rationale: a(a + 6) = 7
=> we have a = 1 or -7
also b(b + 6) = 7
=> b = 1 or -7
given a ≠ b
1) when a =1, b= -7 and a + b = -6
1) when a = -7, b= 1 and a + b = -6
Answer choice B
Answer: B
Question: How many positive even integers less than 100 contain digits 4 or 7?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: One digit numbers: 4
Two digit numbers:
4 at tens place: 40,42,44,46,48
7 at tens place: 70,72,74,76,78
4 at units place: 14,24,34,54,64,84,94 (duplicates removed)
If 7 is at units place, the number cant be even
Total:1+5+5+7= 18
Answer C
Answer: C
Question: The average salary of 15 people in the shipping department at a certain firm is $20,000. The salary of 5 of the employees is $20,000 each and the salary of 4 of the employees is $16,000 each. What is the average salary of the remaining employees?
Options:
A) $19,250
B) $18,500
C) $18,000
D) $15,850
E) $22,600
Rationale: total salary... 15*20k=300k
5 emp @ 20k =100k
4 emp @ 16k =64k
remaing 6 emp sal = 300k-100k-64k =136k
average=136k/6 = 22600
Ans:E
Answer: E
Question: If m=9^(x−1), then in terms of m, 3^(4x−2) must be which of the following?
Options:
A)m/3
B)9m
C)9m^2
D)m^2/3
E)m^2/9
Rationale: 3(4x−2)=3^2(2x−1)=9(2x−1)=9∗9(2x−2)=9∗(9(x−1))2=9m
Answer: C.
Answer: C
Question: Dan's age after 18 years will be 5 times his age 6 years ago. What is the present age of Dan?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Let Dan's present age be x.
x+18 = 5(x-6)
4x = 48
x = 12
The answer is C.
Answer: C
Question: Which of the following CANNOT be the least common multiple of two positive integers x and y
Options:
A)xy
B)x
C)y
D)y - x^2
E)x + y
Rationale: The least common multiple of two positive integers cannot be less than either of them. Therefore, since y - x^2 is less than x, it cannot be the LCM of a x and y.
Answer: D
Answer: D
Question: A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
Options:
A)287
B)27
C)28
D)25
E)28
Rationale: [50/x + 50/(x/2)] – 100/x = 2
x = 25
Answer: D
Answer: D
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)877 m
B)240 m
C)167 m
D)887 m
E)180 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 24)m = 360 m. Let the length of the platform be x meters. Then, (x + 360)/36 = 15
==> x + 360 = 540 ==> x
= 180 m.
Answer: E
Answer: E
Question: Albert is 2 times Mary’s age and 4 times as old as Betty. Mary is 14 years younger than Albert. How old is Betty?
Options:
A)5
B)7
C)10
D)15
E)18
Rationale: A = 2M = M+14
M = 14
A = 28
A = 4B, and so B = 7
The answer is B.
Answer: B
Question: How many words can be formed by using all letters of the word “PACKHORSE”
Options:
A)40320
B)44000
C)42340
D)56000
E)14000
Rationale: The word PACKHORSE contains 8 different letters.
Required number of words = 8p8 = 8! = (8x7x6x5x4x3x2x1) = 40320.
Answer A.
Answer: A
Question: If y is the smallest positive integer such that 3,675 multiplied by y is the square of an integer, then y must be
Options:
A)2
B)5
C)6
D)7
E)12
Rationale: i just tried plugging in the numbers and found out that
12*3675 = 44, 100, which is a square of 210
E
Answer: E
Question: The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of the player is
Options:
A)165 runs
B)170 runs
C)172 runs
D)174 runs
E)None
Rationale: Solution
Let the highest score be x. Then, lowest score =(x-172)
= [(50 x 40)-(x+(x-172)]
= 38 x 48
2x= 2000+172-1824
2x=348
x= 174.
Answer D
Answer: D
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1015. Find the cost of each ice-cream cup?
Options:
A)34
B)76
C)29
D)12
E)20
Rationale: Explanation:
Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 1015
96 + 225 + 490 + 6x = 1015
6x = 204 => x = 34.
Answer:A
Answer: A
Question: A river 2m deep and 45 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is?
Options:
A)6000 M3
B)4580 M3
C)18500 M3
D)4900 M3
E)4700 M3
Rationale: Explanation:
(4000 * 2 * 45)/60 = 6000 M3
Answer: Option A
Answer: A
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 6:30 am. They shall first cross each other at ?
Options:
A)7:15 am
B)7:30 am
C)6: 42 am
D)7:50 am
E)7:60 am
Rationale: Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 6:30 + 12 mins = 6:42
Option C
Answer: C
Question: At what rate percent on simple interest will Rs.750 amount to Rs.950 in 5 years?
Options:
A)3.33%
B)5.93%
C)4.33%
D)5.33%
E)6.33%
Rationale: 200 = (750*5*R)/100
R = 5.33%
ANSWER:D
Answer: D
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)Rs.3250
B)Rs.6250
C)Rs.10250
D)Rs.11750
E)Rs.12000
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
ANSWER:A
Answer: A
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank in gallons is?
Options:
A)100
B)110
C)120
D)140
E)150
Rationale: Let the total time taken by both the pipes be 120 minutes to fill the tank.
Therefore, the number of gallons filled by both the tanks in one minute = (6 + 5) = 11 gallons.
At the same time a waste pipe is also opened which can empty 3 gallons per minute.
Hence, the number of gallons filled in one minute = (11 - 3) = 8 gallons.
Therefore, the number of gallons filled when all the three pipes are opened for 15 minutes = 8 x 15 = 120 gallons.
ANSWER:C
Answer: C
Question: Which number is the odd one out?
159
248
951
357
122
582
Options:
A)951
B)246
C)325
D)147
E)852
Rationale: A
951
In the rest there is the same difference between each digit, eg: 9(Ã¢â‚¬â€œ4) 5 (Ã¢â‚¬â€œ4)1
Answer: A
Question: 150 college students were asked in a survey if they preferred Windows or Mac brand computers. 40 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 40 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
Options:
A)25
B)40
C)70
D)60
E)75
Rationale: 150 = 40(Mac) + x(Window) + 40(both) => x=70
ANSWER:C
Answer: C
Question: In one year, the population, of a village increased by 20% and in the next year, it decreased by 20%. If at the end of 2nd year, the population was 9600, what was it in the beginning?
Options:
A)10000
B)8000
C)1988
D)1277
E)2081
Rationale: x*120/100 * 80/100 = 9600
X*0.96=9600
X=9600/0.96
=> 10000
Answer:A
Answer: A
Question: The price of a T.V. set worth Rs. 8000 is to be paid in 20 installments of Rs. 750 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
A)7250
B)7200
C)7820
D)6000
E)2799
Rationale: Money paid in cash = Rs. 750
Balance payment = (8000- 1000) = Rs. 7250
Answer:A
Answer: A
Question: In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?
Options:
A)20 liters
B)30 liters
C)60 liters
D)29 liters
E)82 liters
Rationale: 2:1 --- 60
1:2
2:4
---------------
3
3 ----------- 60
3 ----------- ? => 60 liters
Answer:C
Answer: C
Question: A man swims downstream 72 km and upstream 45 km taking 6 hours each time; what is the speed of the current?
Options:
A)2.28
B)2.24
C)2.27
D)2.25
E)2.23
Rationale: 72 --- 6 DS = 12
? ---- 1
45 ---- 6 US = 7.5
? ---- 1 S = ?
S = (12 - 7.5)/2 = 2.25
Answer:D
Answer: D
Question: A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price z. The store sold the first 150 copies in the first week at 80% more than z, and then over the next month, sold a 100 more at 20% more than z. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than z. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
Options:
A) 30% loss
B) 10% loss
C) 10% profit
D) 20% profit
E) 60% profit
Rationale: [[z(150)(1.8)+z(100)(1.2)+z(150)(0.6)]/400z] - 1
[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1
[(5.4 + 2.4 + 1.8)/8] - [8/8]
+1.6/8
+20%
answer is D
Answer: D
Question: 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
Options:
A)33
B)34
C)26
D)28
E)19
Rationale: Explanation:
Let the two parts be (54 - x) and x.
Then, 10 (54 - x) + 22x = 780
=> 12x = 240
=> x = 20.
Bigger part = (54 - x) = 34.
Answer: B) 34
Answer: B
Question: The speed of a boat in still water is 40kmph and the speed of the current is 10kmph. Find the speed downstream and upstream?
Options:
A)50,30 kmph
B)40,20 kmph
C)29,25 kmph
D)26,20 kmph
E)12 ,10kmph
Rationale: Speed downstream = 40 + 10
= 50 kmph
Speed upstream = 40 - 10
= 30 kmph
Answer: A
Answer: A
Question: 0.04 x 0.0162 is equal to:
Options:
A)6.48 x 10(power -4)
B)6.84 x 10(power -4)
C)4.68 x 10(power -4)
D)5.48 x 10(power -4)
E)None of them
Rationale: 4 x 162 = 648. Sum of decimal places = 6.
So, 0.04 x 0.0162 = 0.000648 = 6.48 x 10(power -4)
Answer is A.
Answer: A
Question: The average salary/head of all theworkers in a workshop is Rs.850, if the average salary/head of 7technician is Rs.1000 and the average salary/head of the rest is Rs.780, the total no. of workersin the work-shop is ?
Options:
A)18
B)19
C)22
D)26
E)28
Rationale: Let the total number of workers be y.
So sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y -7 workers.
7 x 1000 + 780(y -7) = 850 y
⇒ 7000 + 780y - 5460 = 850y
⇒ 70y = 1540
∴ y = 22
So total number of workers = 22
C
Answer: C
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 800 nuts and 800 bolts?
Options:
A)1,200 seconds
B)1,500 seconds
C)1,750 seconds
D)2,000 seconds
E)3,000 seconds
Rationale: To minimize the amount of time, we should make both machines work all the time while producing 800 nuts and 800 bolts.
Two machines to produce 800 bolts will need (800*1)/2 = 400 seconds.
Two machines to produce 800 nuts will need (800*2)/2 = 8000 seconds.
Total = 400 + 800 = 1,200.
Answer: A.
Answer: A
Question: There are 7 orators A, B, C, D, E, F and G. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
Options:
A)7! / 3!
B)8! / 6!
C)5! x 3!
D)8! / (5! x 3!)
E)8! / (5! x 4!)
Rationale: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.
The remaining 4 people have to be arranged in 4 places.
Thus, 7C3 x 4! = 7!x4!/(4!x3!)=7!/3!
ANSWER:A
Answer: A
Question: If q=4p where p is a prime number greater than 2, how many different positive even divisors does q have, including q?
Options:
A)two
B)three
C)four
D)six
E)eight
Rationale: q=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)
2
4 (because of 2*2)
2p (because of 2 * p)
4p (because of 2 * 2 * p)=C
Answer: C
Question: 1398 x 1398
Options:
A)1954404
B)1981709
C)18362619
D)2031719
E)None of these
Rationale: 1398 x 1398 = (1398)2
= (1400 - 2)2
= (1400)2 + (2)2 - (2 x 1400 x 2)
= 1954404.
Answer: Option A
Answer: A
Question: If * stands for +, / stands for * and + stands for /, then which of the following equations is TRUE?
Options:
A)7*14/7+35-14=-4.2
B)5+7*7-5/14=24
C)14*5/7+35-14=-10.1
D)5/7*7+35-14=4
E)None of these
Rationale: 7*14/7+35-14 will become
7+14*7/35 - 14 = -7 + 14/5 = -21/5 = -4.2
ANSWER:A
Answer: A
Question: A firm has 3 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (2 groups are considered different if at least one group member is different)
Options:
A)64
B)72
C)84
D)96
E)120
Rationale: The total number of ways to form a group of 3 is 9C3 = 84
The number of groups without a senior partner is 6C3 = 20
The number of groups which include a senior partner is 84-20 = 64
The answer is A.
Answer: A
Question: Peter and Rhea lives some distance apart from each other, separated by a straight road. They both take out their cars and start driving at the same time with the same speed towards each other's home.
After some time, their cars meet at 500 miles away from Peter's house. They keep driving and reach at each other's home. Without stopping by, they turn back and start driving again. This time, they meet 300 miles away from each other's home.
What is the distance between their houses?
Options:
A)1200 Miles.
B)110 Miles.
C)1300 Miles.
D)1400 Miles.
E)1500 Miles.
Rationale: Solution:
Let the distance between Peter's (hereafter referred as P) and Rhea's (hereafter referred as R) be D.
When P and R meet for the first time, P has traveled 500 miles.
In that case, R has traveled (D - 500) miles.
=> Speed of P / Speed of R = 500 / (D - 500) ...... (1)
When P and R meet for the second time, P has traveled (D - 500) + 300 miles
Now, R has traveled (500 + D - 300)
=> Speed of P / Speed of R = 5 / (D - 5) ..... (2)
Equating (1) and (2)
500 / (D - 500) = (D - 2) / (D + 2)
D = 1200 Miles.
Answer A
Answer: A
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 20 gallons of gasoline?
Options:
A)190
B)284.6
C)300
D)244
E)312
Rationale: so 12.2 * 20 = 244..
IMO option D is correct answer..
Answer: D
Question: R-R-R-G-G-G-Y-Y-B-R-R-R-G-G-G-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?
Options:
A)62
B)63
C)64
D)65
E)66
Rationale: The repeated pattern R-R-R-G-G-G-Y-Y-B has 9 beads.
But the missing section includes R-R-R-G-G-G-Y-Y at the end.
Thus the number of beads in the missing section has the form 9k + 8.
The answer is A.
Answer: A
Question: If 4 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
Options:
A)(4x + 2y)/5
B)(4x + 2y)/(x + y)
C)(4x + 2y)/(xy)
D)5(4x + 2y)
E)4x + 2y
Rationale: Total Cost = Weight(in pounds) * Price/pound;
To find Total cost/pound, Divide by total pounds.
Cost of Dried apricots = 4x;
Cost of prunes = 2y;
Cost per pound = (4x + 2y)/5;
Ans is (A).
Answer: A
Question: Once I had been to the post office to buy five-rupee, two-rupee and one-rupee stamps. I paid the clerk Rs. 20, and since he had no change, he gave me three more one-rupee stamps. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought ?
Options:
A)10
B)9
C)12
D)8
E)4
Rationale: Explanation :
At least two stamps of each type were ordered initially.
So, Rs.2 ( 5 + 2 + 1 ) = Rs.16 have been spent.
That leaves ( 20 – 16 ) = Rs.4.
In this Rs.4, three more stamps of one rupee were given, thus accounting for Rs.19 in all.
Since, one more rupee remains, it means that one more stamps of Rs.1 were bought initially.
So the total number of stamps is 2(of Rs.5) + 2(of Rs.2) + 6(of Rs.1). i.e 10.
Answer : A
Answer: A
Question: Three unbiased coins are tossed. What is the probability of getting at most two heads?
Options:
A)3/4
B)1/4
C)7/8
D)3/8
E)2/8
Rationale: Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) =	n(E)	=	7	.
n(S)	8
Answer : C.
Answer: C
Question: What number has a 5:1 ratio to the number 13?
Options:
A)22
B)50
C)88
D)65
E)12
Rationale: 5:1 = x: 13
x = 65
Answer: D
Answer: D
Question: The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?
Options:
A)19
B)20
C)1
D)0
E)25
Rationale: Avg of 20 nos = 0
sum of 20 numbers/20 = 0
sum of 20 nos = 0
=>19 positive nos
ANSWER A
Answer: A
Question: In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ?
Options:
A)20
B)25
C)30
D)Data inadequate
E)None of these
Rationale: In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively.
say 3x and 2x respectively.
If the number of boys participating in the sports is 15,no of girls participating in sports = 10.
Total students participating out of 60 in class = 15+10=25
Total students not participating out of 60 in class = 60-25=35
The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports.
so out of 45 not participating in sports, 20 are girls and 15 are boys.
No of girls in class = 20+10=30
ANSWER:C
Answer: C
Question: Lisa earns a profit of $3 on each ribbon that she sells, and $5 on each bracelet. If at the end of the day Lisa has earned $120 and she has sold at least 10 pieces of each item. At least how many bracelets she has sold?
Options:
A)2
B)5
C)9
D)12
E)15
Rationale: Since Lisa has sold at least 10 pieces for each item, let us say Lisa sells (10 + r) number of ribbons and (10 + b) number of bracelets, her profit for the day = 3(10 + r) + 5(10 + b)
=> 3(10 + r) + 5(10 + b) = 120
=> 30 + 3r + 50 + 5b = 120
=> 3r + 5b = 120 - 30 - 50 = 40
=> 5b = 40 - 3r
=> b = 8 - (3/5)r
To minimize b, we need to maximize r and it will be a multiple of 5.
r = 5, b = 8 - (3/5)5 = 5
r = 10, b = 8 - (3/5)10 = 2
Beyond that b will become -ve. So Lisa has sold at least 10 + 2 = 12 bracelets.
Answer: D
Answer: D
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 14000, then find the annual income of A?
Options:
A)Rs. 420000
B)Rs. 180000
C)Rs. 201600
D)Rs. 470400
E)None of these
Rationale: B's monthly income = 14000 * 112/100 = Rs. 15680
B's monthly income = 2 parts ----> Rs. 15680
A's monthly income = 5 parts = 5/2 * 15680 = Rs. 39200
A's annual income = Rs. 39200 * 12 = Rs. 470400
ANSWER:D
Answer: D
Question: If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $61, how much does one shirt cost?
Options:
A)$9
B)$12
C)$13.20
D)$15
E)$16.80
Rationale: 3J + 2S = 69
2J + 3S = 61
----------------
5J + 5S = 130 ----(divide by 5)---> J + S = 26
3J + 2S = J + 2(J + S) = J + 52 = 69 ---> J = 17
3*17 + 2S = 69
51 + 2S = 69
2S = 18
S = 9
Answer: A
Answer: A
Question: Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 2/3 of the juniors is equal to 1/2 of the seniors, what fraction of the students in the room are juniors?
Options:
A)3/20
B)1/3
C)3/7
D)2/7
E)7/2
Rationale: Let total number of juniors= J
total number of seniors =S
(2/3) J = (1/2) S
=> S = 4/3 J
Total number of students = J+S = (7/3) J
Fraction of the students in the room are juniors = J/(J+S) = J/[(7/3) J]
=3/7
Answer C
Answer: C
Question: If x is a positive integer, which of the following must be odd?
Options:
A)x+1
B)x^2+x
C)x^2+x+5
D)x^2−1
E)3x^2−3
Rationale: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 5 = ODD
Hence C.
Answer: C
Question: log3 N+log9 N what is 3 digit number N that will be whole number
Options:
A)629
B)729
C)829
D)929
E)727
Rationale: No of values N can take is 1
9^3=729
ANSWER:B
Answer: B
Question: What least number must be added to 3000 to obtain a number exactly divisible by 19 ?
Options:
A)2
B)19
C)9
D)4
E)8
Rationale: On dividing 3000 by 19, we get 17 as remainder.
Number to be added = (19 - 17) = 2.
ANSWER A 2
Answer: A