divelab/Sys2Bench huggingface dataset:
Question: At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Dhoni ,Kamal, Baskar, and Dinesh get lockers with the numbers 100, 400, 150, and 25, respectively, who is the most popular student?
Options:
A)Dhoni
B)Baskar
C)Kamal
D)Dinesh
E)They have equal popularity
Rationale: Distinct prime factors of 100 (Dhoni) : 2,5
Distinct prime factors of 400 (Kamal): 2 and 5.
Distinct prime factors of 150 (Baskar): 2,3, and 5
Distinct prime factors of 25 (Dinesh): 5.
So most popular student - Dinesh
Answer B
Answer: B
Question: A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many acres Q were used for corn?
Options:
A) 188
B) 258
C) 376
D) 470
E) 517
Rationale: consider 5x acres of land used for bean
consider 2x acres of land used for wheat
consider 4x acres of land used for corn
Total given is 1034 acres
11x =1034
x = 94
land used for corn Q= 4 * 94 = 376
correct option - C
Answer: C
Question: n denotes the number obtained when n is rounded to the nearest tenth.
For example 4.31 = 4.3
0.089 - 1.135 =
Options:
A)1.05
B)1.04
C)-1.05
D)-1.0
E)-0.1
Rationale: Here Let the first quantity be A=> A rounded to nearest tenths => 0.1
Similarly let the second quantity be B => B rounded to nearest tenths => 1.1=> A-B=0.1-1.1=-1
Hence A-B=-1
ANSWER:D
Answer: D
Question: Jim began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Jim?
Options:
A)35
B)55
C)39
D)40
E)60
Rationale: Carla starts 30 minutes later and it takes 3 hr for carla to meet Jim
So Jim total time travelled = 3hr + 30 minutes
Jim distance = 30 * (3 1/2) = 105
so carla need to travle 105 to meet Jim in 3 hrs
speed of carla = 105/3 = 35 miles per hour
Answer is A
Answer: A
Question: (2-x)^(x^2)=1^3x
What is the value of x ?
Options:
A)2
B)3/2
C)1
D)3
E)0
Rationale: (2-x)^(x^2)=1
2-x=1
x = 1
Ans: C
Answer: C
Question: City A to city B, Andrew drove for 1hr at 46 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
Options:
A)56.5
B)57.5
C)61
D)61.5
E)62.5
Rationale: The total distance is 1×46+3×60=226
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=226/4=56.5
A
Answer: A
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
Options:
A)12/145
B)36/145
C)11/145
D)31141
E)None
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: B
Question: A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 20 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
Options:
A) $0
B) $3
C) $4
D) $12
E) $15
Rationale: Actual Cost = $60
SP = Actual Cost + Mark up
= Actual Cost + 20% SP
= 60*100/80
on sale SP = 80/100(60*100/80) = 60
Gross profit = $0
Answer is A
Answer: A
Question: Mary travels the first 9 hours of her journey at 40 mph speed and the remaining 6 hours at 30 mph speed. What is the average speed of Mary's travel in mph?
Options:
A)32 mph
B)34 mph
C)36 mph
D)35 mph
E)31 mph
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by mary = Distance covered in the first 9 hours + Distance covered in the next 6 hours.
Distance covered in the first 9 hours = 9Ã—40=360 miles
Distance covered in the next 6 hours= 6Ã—30=180 miles
Therefore, total distance travelled = 360+180=540 miles.
The total time taken = 9+6=15hours.
Hence, the average speed =540/15= 36 mph.
Answer : C
Answer: C
Question: For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 220 true?
Options:
A)1
B)3
C)5
D)6
E)9
Rationale: Answer D
(a+b)(a-b)=220
6cases For (a+b), (a-b)
220, 1
110, 2
55, 4
44,5
22, 10
20,11
Answer D
Answer: D
Question: Instead of multiplying a number by 9, the number is divided by 9. What is the percentage of error obtained ?
Options:
A)97.765%
B)99.765%
C)96.765%
D)95.765%
E)98.765%
Rationale: let the number be x
the right number is 9x
the wrong number is x/9
error is(9x-x/9)=80x/9
percentage of error is((80x/9)/9x)*100=98.765%
ANSWER:E
Answer: E
Question: Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 5. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?
Options:
A)3, 8, 24
B)7, 9, 17
C)6, 9, 12
D)5, 15, 18
E)9, 10, 13
Rationale: I didnt get your point on eliminating C.
The number of stamps only one purchased was divisible by 5.Could that not be Cecilia with 9 stamps.
I choose this and marked C.
Answer: C
Question: The length of a side of a hexagon is 10 inches. What is the perimeter?
Options:
A)10
B)20
C)30
D)40
E)60
Rationale: Hexagon. It means 6 equal sides.
p = 6(10)= 60 inches
Answer E
Answer: E
Question: A positive number x is multiplied by 8, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
Options:
A) 9/4
B) 3/2
C) 8/3
D) 2/3
E) 1/2
Rationale: sq rt(8x/3) = x
=> 8x/3 = x^2
=> x = 8/3
Ans - C
Answer: C
Question: Two pipes A and B can fill a cistern in 20 and 40 minutes respectively, and a third pipe C can empty it in 80 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
A)19 1/7 min
B)15 1/7 min
C)17 1/7 min
D)7 1/7 min
E)16 min
Rationale: 1/20 + 1/40 - 1/80 = 5/80
80/5 = 16
ANSWER:E
Answer: E
Question: A pharmaceutical company received $3 million in royalties on the first $30 million in sales of and then $9 million in royalties on the next $120 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $30 million in sales to the next $120 million in sales?
Options:
A)8%
B)15%
C)25%
D)52%
E)56%
Rationale: (9/120)/(3/30) = 3/4 = 75% it means that 9/120 represents only 75%. Therefore a decrease of 25%.
Answer C
Answer: C
Question: A train covers a distance of 12 km in 10 min. If it takes 16 sec to pass a telegraph post, then the length of the train is?
Options:
A)320 m
B)188 m
C)120 m
D)178 m
E)189 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 16
= 320 m.
Answer:A
Answer: A
Question: 100 white and black tiles will be used to form a 20x20 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
Options:
A)75
B)70
C)85
D)90
E)95
Rationale: Answer = B
Please refer diagram below
90 - 20 = 70
Answer: B
Question: Find the remainder T when 12^190 is divided by 1729 ?
Options:
A)12
B)1
C)1728
D)1717
E)4
Rationale: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder T-1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Answer: D
Question: A mixture of 120 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Options:
A)2 liters
B)3 liters
C)8 liters
D)5 liters
E)7 liters
Rationale: Number of liters of water in120 liters of the mixture = 20% of 120 = 20/100 * 120 = 24 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (24 + P) and total volume of mixture is (120 + P).
(24 + P) = 25/100 * (120 + P)
96+4P = 120+P
P = 8 liters.
Answer: C
Answer: C
Question: Twelve dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 12 dots that do not form an equilateral triangle?
Options:
A)208
B)212
C)216
D)220
E)224
Rationale: The total number of ways we can choose three dots is 12C3=220.
We can form four equilateral triangles from these twelve dots.
There are 220 - 4 = 216 combinations which do not form an equilateral triangle.
The answer is C.
Answer: C
Question: There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?
Options:
A)m/4
B)m/2
C)3m/4
D)m
E)4m/5
Rationale: now it is 1:6:5:4..
let the common ratio be x, then total number = (1+6+5+4)*x...
but earlier all were distributed equally among all four =16x/4=4x
so m=4/x OR x=m/4
what was the balls moved 4x-x=3x.. 4x was initial and present is 1*x
so 3x=3∗m/4=3 m/4
ANSWER:C
Answer: C
Question: Which of the following will divide evenly into 507,406,520?
Options:
A)13
B)11
C)9
D)3
E)4
Rationale: Rule:
4: Last two digits should be divisible by 4
the last two digits are 00, which are divisible by 4
Answer: E
Answer: E
Question: In a class there are 20 boys and 20 girls. In how many ways can a boy and a girl be selected?
Options:
A)400
B)500
C)600
D)530
E)630
Rationale: Explanation:
We can select one boy from 20 boys in 20 ways.
We select one girl from 20 girls in 20 ways
We select a boy and girl in 20 * 20 ways i.e., = 400 ways.
Answer: Option A
Answer: A
Question: A circular well with a diameter of 2 metres, is dug to a depth of 4 metres. What is the volume of the earth dug out?
Options:
A)26 m³
B)28 m³
C)44 m³
D)46 m³
E)None
Rationale: Sol.
Volume = ∏r²h = [22/7 * 1 * 1 * 14] m³ = 44m³
Answer C
Answer: C
Question: If x^6 > x^9 > x^7, which of the following could be the value of x?
Options:
A)-6
B)-1/2
C)2
D)1/2
E)6
Rationale: x^6 > x^7 > x^9
1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x.
This can be possible only if the base is negative; therefore, the variable, x, must be a negative number.
2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1.
With this information, we know that x is a negative number between 0 and -1; therefore, B (-1/2) is the only option.
Answer: B
Question: A grocer has a sale of Rs. 8435, Rs. 8927, Rs. 8855, Rs. 9230 and Rs. 8562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 8500?
Options:
A)s. 1991
B)s. 2991
C)s. 3991
D)s. 4991
E)s. 6991
Rationale: Explanation:
Total sale for 5 months = Rs. (8435 + 8927 + 8855 + 9230 + 8562) = Rs. 44009.
Required sale = Rs. [ (8500 x 6) â€“ 44009 ]
= Rs. (51000 â€“ 44009)
= Rs. 6991.
Answer E
Answer: E
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine K is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine K can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
Options:
A)14
B)13
C)11
D)9
E)7
Rationale: 'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.
To finish a work say Machine K you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D
Answer: D
Question: Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 17 candidates. She plans to have one working interview with 3 of the 17 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?
Options:
A)720
B)420
C)300
D)30
E)333
Rationale: 420.
Answer B
Answer: B
Question: Three numbers are in the ratio 3:5:7. The largest number value is 56. Find difference between Smallest & largest number is?
Options:
A)34
B)20
C)36
D)32
E)30
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 56
= The largest number is = 7
= Then 7 parts -----> 56 ( 7 * 8 = 56 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 32 (4 * 8 = 32)
D
Answer: D
Question: The population of a town increased from 1,34,000 to 2,32,500 in a decade. The average percent increase of population per year is:
Options:
A)4.37%
B)7.3%
C)7.6%
D)8.75%
E)None
Rationale: Explanation: Increase in 10 years = (232500 - 134000) = 98500.
Increase% = (98500/134000 x 100)% = 73%.
Required average = (73/10)% = 7.3%.
Answer: Option B
Answer: B
Question: A car crosses a 720 m long bridge in 2 minutes. What is the speed of car in km per hour?
Options:
A)20.5 km/hr
B)21.6 km/hr
C)31.6 km/hr
D)15.6 km/hr
E)22.3 km/hr
Rationale: Speed = 720	m/sec.
360/60m/s
= 6 m/sec.
Converting m/sec to km/hr (see important formulas section)
=6 x	18/5 km/hr
5
= 21.6 km/hr
B
Answer: B
Question: Sara has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
Options:
A) 32
B) 30
C) 29
D) 28
E) 27
Rationale: 5a + 10b = 460
a> b
Pick an easy number to work with.
suppose a=30.
Then you have 150.
You need another 310 and that means you need b=31 which is greater than a.
Therefore, a > 30.
The only answer choice where a > 30 is if a = 32.
A is the answer.
Answer: A
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)18
B)16
C)17
D)19
E)13
Rationale: Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).
Answer:D
Answer: D
Question: P and Q started a business investing Rs 75000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
Options:
A)5:1
B)17:3
C)5:6
D)17:7
E)3:8
Rationale: Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 75000:15000
= 75:15
= 5:1
Option A
Answer: A
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
Options:
A)6 hrs 21 min
B)6 hrs 81 min
C)6 hrs 91 min
D)8 hrs 21 min
E)6 hrs 51 min
Rationale: Time taken to cover 600 km = 600/100
= 6 hrs.
Number of stoppages
= 600/75 - 1 = 7
Total time of stoppages
= 3 * 7
= 21 min
Hence, total time taken
= 6 hrs 21 min.
Answer: A
Answer: A
Question: The sum of four consecutive even numbers is 292. What would be the smallest number?
Options:
A)49
B)68
C)60
D)57
E)70
Rationale: E
70
Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
Answer: E
Question: 5 3 -2 -5 -3 2....What is the sum of first thirty number sequence?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2
=> 50-50=0.
ANSWER:A
Answer: A
Question: In an examination, the percentage of students qualified to the students appeared from school 'P' is 70%. In school 'Q', the number of students appeared is 30% more than the students appeared from school 'P' and the number of students qualified from school 'Q' is 50% more than the students qualified from school 'P'. What is the % of students qualified to the number of students appeared from school 'Q' ?
Options:
A)80.78%
B)80.76%
C)80.72%
D)80.79%
E)80.74%
Rationale: Explanation:
Number of students appeared from school 'P' = 100, say
Number of students qualified from school 'P' = 70
and Number of students appeared from school 'Q' = 130
Number of students qualified from school 'Q' = 50% more than those qualified from school 'P'.
= 70 + 35 = 105 % of students qualified to the number of students appeared from school B = 105 / 130 * 100
= 80.76%
ANSWER: B
Answer: B
Question: The average height of 30 girls out of a class of 40 is 160 cm. and that of the remaining girls is 156 cm. The average height of the whole class is :
Options:
A)158 cms
B)158.5 cms
C)159 cms
D)159.5 cms
E)none
Rationale: Explanation:
Average height of the whole class =(36×160+10×156/40)=159 cms
Answer C
Answer: C
Question: Find a sum for first 9 prime numbers?
Options:
A)22
B)28
C)29
D)82
E)100
Rationale: Required sum = (2 + 3 + 5 + 7 + 11+13+17+19+23) = 100
Note: 1 is not a prime number
OptionE
Answer: E
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)19
B)26
C)18
D)17
E)12
Rationale: 9 * 2 = 18 years
Answer: Option C
ExplanaC
Answer: C
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
Options:
A)7
B)6
C)5
D)9
E)1
Rationale: Explanation:
C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs. 6/5
For Rs. 6/5, toffees sold = 6. For re. 1.
Toffees sold = 6 * 5/6 = 5
Answer: C
Answer: C
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
13 * 15 * 17 =?
Options:
A)89
B)49
C)68
D)268
E)55
Rationale: D
268
(17 * 15) + 13 = 268
Answer: D
Question: If the city centers of Tokyo and London are 5936 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.)
Options:
A)1.7 × 10^7
B)4.9 × 10^7
C)3.8 × 10^8
D)2.6 × 10^9
E)1.2 × 10^10
Rationale: 5936 miles = 5936 x 5280 feet/mile x 12 inches/foot which is about 3.8 x 10^8 inches.
The answer is C.
Answer: C
Question: a, b, c and d are four consecutive numbers. If the sum of a and dis 103, what is the product of b and c?
Options:
A)2652
B)2578
C)2534
D)3354
E)4234
Rationale: A
2652
Here d = a + 3
a + a + 3 = 103
2a = 100
a = 50
So, numbers are 50, 51, 52 and 53
∴ b × c= 51 × 52 = 2652
Answer: A
Question: From the word 'TEA', how many independent words can be made with-out changing the order of the letters and using each letter only once ?
Options:
A)0
B)8
C)3
D)2
E)9
Rationale: Explanation:
The words formed are
Answer: A) 0
Answer: A
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum ?
Options:
A)Rs 4462.50
B)Rs. 8032.50
C)Rs. 8900
D)Rs. 8925
E)None
Rationale: Solution
Principal = Rs. (100*4016.25/9*5)= Rs.(401625/45) =Rs.8925
Answer D
Answer: D
Question: . In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 70 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
Options:
A) 50%
B) 53%
C) 54%
D) 55%
E) 57%
Rationale: Registered voters = 100
D = 60
R = 40
70% of D ( 60) = 42
20% of R ( 40 ) = 8
Total voter% of registered voters = 50 / 100
50% Ans A
Answer: A
Question: A man rows to a place 48 km distance and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
Options:
A)1 km/hr
B)2.5 km/hr
C)3 km/hr
D)4 km/hr
E)None
Rationale: Sol.
Suppose he moves 4 km downstream in x hours. Then,
Speed downstream = [4/x] km/hr, Speed upstream = [3/x] km/hr.
∴ 48/(4+x) + 48/(3/x) = 14 or x = 1/2.
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = 1/2 (8-6) km/hr = 1 km/hr.
Answer A
Answer: A
Question: How many bricks, each measuring 25cm*11.25cm*6cm, will be needed to build a wall 8m*6m*22.5m
Options:
A)6400
B)3777
C)2679
D)2667
E)1997
Rationale: To solve this type of question, simply divide the volume of wall with the volume of brick to get the numbers of required bricks
So lets solve this
Number of bricks =
Volume of wall/Volume of 1 brick=800∗600∗22.5/25∗11.25∗6=6400
Answer: A
Answer: A
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1996. She ended on her
Options:
A)a) thumb
B)b) the index finger
C)c) the middle finger
D)d) the ring finger
E)e) the little finger
Rationale: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1996 has to be the ring finger
Answer is (D)
Answer: D
Question: If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
Options:
A)80%
B)30%
C)90%
D)40%
E)42%
Rationale: 8 = (1*20*R)/100
R = 40%
Answer:D
Answer: D
Question: The average age of 10 men increases by 6 years when two women are included in place of two men of ages 18 and 22 years. Find the average age of the women?
Options:
A)37
B)26
C)30
D)50
E)11
Rationale: Explanation:
18 + 22 + 10 * 6 = 100/2 = 50
Answer: D
Answer: D
Question: Ella picked a number of pears, each of which she sold, canned, or poached. If she canned 60 percent more than she poached, and she poached 10 percent less than she sold. If there were a total of 501 pears, then how many pears did she sell?
Options:
A)130
B)135
C)140
D)145
E)150
Rationale: Let x be the amount of pears that she sold.
Then she poached 0.9x.
Then she canned 1.6*0.9x=1.44x.
The total amount of pears is x+0.9x+1.44x=3.34x
The fraction of pears that she sold is 1/3.34=100/334=50/167.
The number of pears she sold is (50/167)*501=150.
The answer is E.
Answer: E
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Options:
A)2.9
B)2.2
C)2.5
D)2.1
E)2.3
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer:C
Answer: C
Question: One-seventh of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
Options:
A)2.3%
B)3.4%
C)4.5%
D)5.6%
E)6.7%
Rationale: 1/7 of the switches are defective.
The defective switches that are not rejected are 1/5*1/7 = 1/35 = 4/140 of all switches.
The non defective switches that are sold are 6/7*19/20 = 114/140 of all switches.
The percent of switches sold that are defective is 4/118 which is about 3.4%.
The answer is B.
Answer: B
Question: Which of the following inequalities is equivalent to 11 - 11x > 133?
Options:
A) x > -2
B) x > -1
C) x > -3
D) x > -11
E) x > -5
Rationale: You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide by a negative number, the sign of the inequality flips.
To illustrate,
11 - 11x > 133
11x > -122 (Correct)
x > -11 (Correct)
the correct option is D
Answer: D