divelab/Sys2Bench huggingface dataset:
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 1. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
Options:
A){3, 4, 5, 10, 14}
B){3, 6, 7, 10, 12}
C){3, 5, 5, 10, 16}
D){1, 5, 7, 10, 12}
E){5, 8, 9, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 8 to 10 + 2*{SD} = 12.
A. {3, 4,5, 10, 14} --> only 1 number is in this range. Discard.
B. {3,6, 7, 10, 12} --> only 2 numbers are in this range. Discard.
C. {3,5, 5, 10, 16} --> only 1 number is in this range. Discard.
D. {1,5, 7, 10, 12} --> only 2 numbers are in this range. Discard.
E. {5, 8, 9, 10, 12} --> 4 numbers are in this range. OK.
Answer:E.
Answer: E
Question: On increasing the number of lines in a page by 100, they become 240. What is the % of increase in the no. of lines in the page?
Options:
A)20%
B)305
C)50%
D)71.4%
E)60%
Rationale: Explanation : Number of pages increased = 100
Now , the number of pages of book = 240
Number of pages of the books before increase = 240 – 100 = 140
% increase in the number of pages in the book = 100 /140
x 100% = 71.4%
D
Answer: D
Question: A man has $480 in the denominations of one-Dollar, five-Dollar notes and ten-Dollar. The number of Dollars of each denomination is equal. What is the total number of Dollar that he has ?
Options:
A)50
B)60
C)90
D)48
E)67
Rationale: C
$90
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer: C
Question: Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 72 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)11 : 6
B)12 : 7
C)13 : 7
D)65 : 36
E)13 : 6
Rationale: Sol. Distance travelled by Car A = 65 Ã— 8 = 520 km
Distance travelled by Car B = 72 Ã— 4 = 288 km
Ratio = 520/288 = 65 : 36
D
Answer: D
Question: The side of a square is increased by 25% then how much % does its area increases?
Options:
A)55.2 %
B)10 %
C)15 %
D)56.25 %
E)18 %
Rationale: Explanation:
a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer : D
Answer: D
Question: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 24, what is the remainder when k is divided by 7?
Options:
A)2
B)5
C)6
D)3
E)8
Rationale: Cant think of a straight approach but here is how I solved it:
K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)
so the possible values of K = {2, 7, 12, 17, 22} (less than 24)
Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5
so the possible value set for k = {5, 11, 17, 23} (less than 24)
17 is the only common number in both the sets. Hence k = 17
Answer : D
Answer: D
Question: Health insurance Plan C requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
Options:
A)$600
B)$1000
C)$3800
D)$5300
E)$6200
Rationale: 0.5 * 600 = 300 where C = B.
Answer: B
Question: Which of these fractions is equivalent to 15
25?
Options:
A)3/4
B)2/3
C)3/5
D)1/2
E)5/7
Rationale: Both the numerator and the denominator are divisible by 5.
Dividing, we get 15/25 = 15/5/25/5 = 3/5 . Therefore, 15/25 is equivalent to 3/5 .
correct answer C
Answer: C
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)16
B)18
C)19
D)22
E)24
Rationale: Explanation:
10 * 15 + 36 – 26 = 160/10 = 16
A)
Answer: A
Question: In an examination 40% failed in Hindi, 45% failed in English. If 25% students failed in both the subjects. Then the percentage of failed students is?
Options:
A)60
B)20
C)25
D)30
E)40
Rationale: 15+25+20 = 60
ANSWER A
Answer: A
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 14% per annum then the gain of B in a period of 3 years is?
Options:
A)400
B)410
C)460
D)420
E)430
Rationale: (3500*4*3)/100 => 420
Answer: D
Answer: D
Question: 4/[(1/0.03) + (1/0.37)] = ?
Options:
A)0.004
B)0.11111
C)2.775
D)3.6036
E)36.036
Rationale: Approximate.
1/.03 = 100/3 = 33
1/.37 = 100/37 = 3
Denominator becomes 33 + 3 = 36
4/36 = .1111
Answer (B)
Answer: B
Question: In an examination 60% failed in Math and 40% failed in French. If 32% failed in both. What % of students passed in both.
Options:
A)25%
B)15%
C)20%
D)32%
E)10%
Rationale: Passed in Math = 100 - 60 = 40%
Passed in French = 100 - 40 = 60%
Students who passed Math or French = 100 -32 = 68%
Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-68 =32%
ANSWER:D
Answer: D
Question: If y exceeds x by 30%, then x is less than y by?
Options:
A)23 2/8%
B)16 8/3%
C)23 1/13%
D)76 2/3%
E)23 2/3%
Rationale: X=100	y=130
130------30
100-------? => 23 1/13%
Answer:C
Answer: C
Question: The average of 11 results is 40, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
Options:
A)165
B)166
C)167
D)168
E)169
Rationale: 1 to 11 = 11 * 40 = 440
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 440 = 169
ANSWER:E
Answer: E
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rose ’s and Tom ’s share in the profit?
Options:
A)Rs.340
B)Rs.362
C)Rs.370
D)Rs.382
E)Rs.390
Rationale: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 3982 × 1/11 = Rs.362.
B)
Answer: B
Question: A computer factory produces 6048 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month?
Options:
A)2.25.
B)3.125.
C)4.5.
D)5.225.
E)6.25.
Rationale: Number of hours in 28 days = 28*24
Number of 30 mins in 28 days = 28*24*2
Number of computers built every 30 mins = 6048/( 28*24*2) = 4.5
Answer C
Answer: C
Question: The volume of a cube is 1000 cc. Find its surface.
Options:
A)864
B)556
C)255
D)600
E)267
Rationale: a3 = 1000 => a = 10
6a2 = 6 * 10 * 10 = 600
Answer:D
Answer: D
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
Options:
A)22 hours
B)21 hours
C)23 hours
D)20 hours
E)28 hours
Rationale: D
20 hours
|-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: D
Question: A 2015 model car had an average mileage of 38 miles per gallon, when the car wight was 180 kilograms. An upgraded version of the car in 2016 gave a mileage of 43 miles per gallon and the car weight was reduced to 150 kilograms. By approximately what percent did the mileage of the car to the weight of the car improve?
Options:
A)28
B)43
C)36
D)19
E)37
Rationale: Initial mileage/weight ratio = 38/180 = 190/900
Revised mileage/weight ratio = 43/150 = 258/900
Answer: C
Answer: C
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 11 a.m.?
Options:
A)5
B)6
C)7
D)8
E)15
Rationale: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour
Time duration from 8 am to 11 am = 3 hours
Hence they cross each other 15 times before 11 am
Answer is E
Answer: E
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 1100 m long?
Options:
A)200 Sec
B)230 Sec
C)167 Sec
D)197 Sec
E)179 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2300 m
T = D/S
T = 2300/10
T = 230 Sec
Answer: B
Answer: B
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)21/115
B)36/145
C)31/111
D)11/154
E)11/151
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: The ratio between the sale price and the cost price of an article is 9:5. What is the ratio between the profit and the cost price of that article?
Options:
A)23
B)1:2
C)4:5
D)3:5
E)25
Rationale: C.P. = Rs. 5x and S.P. = Rs. 9x.
Then, Gain = Rs. 4x
Required ratio = 4x : 5x = 4:5
C
Answer: C
Question: John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 4% and the mobile phone at a profit of 20%. Overall how much he make aprofit.
Options:
A)s. 190
B)s. 1120
C)s. 1200
D)s. 1250
E)s. 1290
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 20/100) = 8000 + 1600
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 1600 = Rs. 1200
As this is positive, an overall profit of Rs. 1200 was made.
C
Answer: C
Question: How many numbers from 10 to 47 are exactly divisible by 3?
Options:
A)12
B)15
C)16
D)17
E)18
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,.
12 Numbers.
10/3 = 3 and 47/3 = 15 ==> 15 - 3 = 12. Therefore 12 digits
A)
Answer: A
Question: If n is an integer and 101n^2 is less than or equal to 3600, what is the greatest possible value of n?
Options:
A)7
B)5
C)9
D)10
E)11
Rationale: 101 * n^2 <=3600
n^2 <=3600/101 which will be less than 81 since 3600/100 = 36 which is the square of 9
Next closest value of n where n^2<=36 is 5
Ans B
Answer: B
Question: A man saves Rs 350 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
Options:
A)Rs 1159.54
B)Rs 1158.54
C)Rs 1158.78
D)Rs 1158.88
E)None of these
Rationale: Explanation:
=[350(21/20Ã—21/20Ã—21/20)+350(21/20Ã—21/20)+350(21/20)]=1158.54
Option B
Answer: B
Question: A farmer is planting a row consisting of 3 unique apple trees and 3 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?
Options:
A)72
B)576
C)1,024
D)1,152
E)10,080
Rationale: 2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
4 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *3! * 3! = 72
correct answer option A
Answer: A
Question: .The price of commodity P increases by 40 paise every year, while the price of commodity Q increases by 15 paise every year. If in 2001, the price of commodity P was Rs. 4.20 and that of Q was Rs. 6.30, in which year commodity P will cost 40 paise more than the commodity Q ?
Options:
A)2008
B)2009
C)2010
D)2011
E)None of these
Rationale: Explanation :
Let the commodity P costs 40 paise more than the commodity Q after n years
Price of the commodity P in 2001 = Rs.4.20
Since the price of the commodity P increases by Rs 0.40 every year,
Price of the commodity P after n years from 2001 = Rs.4.20 + (n × .40)
Price of the commodity Q in 2001 = Rs.6.30
Since the price of the commodity Q increases by Rs 0.15 every year,
price of the commodity Q after n years from 2001 = Rs.6.30 + (n × .15)
Since the commodity P costs Rs. 0.40 more that the commodity Q after n years from 2001,
4.20 + (n × .40) = 6.30 + (n × .15) + 0.40
=> (40n - .15n) = 6.30 - 4.20 + 0.40 = 2.5
=> .25n = 2.5
⇒ n = 2.5/.25 = 250/25 = 101.15¯
=> Commodity P costs Rs.0.40 more that the commodity Q after 10 years from 2001. i.e., in 2011. Answer : Option D
Answer: D
Question: If f(2, 4) = 24 and f(1, 5) = 26, what is the value of f(2, 6)?
Options:
A)107
B)127
C)44
D)None of these
E)Cannot be determined
Rationale: Solution:
The function f(a, b) = a3 + b2
f(2, 4) therefore is = 8 + 16= 24 and
f(1,5) = 1 +25= 26
Therefore, f(2, 6) = 8 + 36 = 44
Answer C
Answer: C
Question: At what rate percent of simple interest will a sum of money double itself in 12 years?
Options:
A)8 1/7 %
B)8 1/3 %
C)8 7/3 %
D)6 1/3 %
E)8 9/3 %
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 12)
= 25/3 = 8 1/3 %
Answer: B
Answer: B
Question: For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3).
If 3x = –25, then x =
Options:
A) –15
B) –2
C) -3
D) 6
E) 15
Rationale: (3+2)(x-3)=-25..
x-3=-5..
x=-2
B
Answer: B
Question: A person travels from P to Q a speed of 60 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
Options:
A)33
B)75
C)48
D)99
E)21
Rationale: Speed on return trip = 150% of 60 = 90 km/hr.
Average speed of trip = 60 + 90 /2 = 150/2 = 75 km/hr
Answer : B
Answer: B
Question: There are 8 books in a shelf that consist of 1 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Options:
A)35
B)45
C)50
D)55
E)60
Rationale: 8C4 [Select any four] - 7C4 [Select all hard backs] = 35.
A
Answer: A
Question: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $158.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?
Options:
A)$21
B)$27
C)$31
D)$43
E)It cannot be determined
Rationale: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:
3B+7S+C=120
4B+10S+C=158.5
Subtracting the first equation from the second gives us B+3S=38.5
Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=43. In any case, there is no necessity to know each item's price, just the sum.
Answer: D
Answer: D
Question: In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: let no. of buffaloes be x & no. of ducks be y
buffaloes have 4 legs while ducks have 2
4x + 2y = 2*(x + y) + 24
=> 4x + 2y - 2x - 2y = 24
=> x = 12
number of buffaloes in the group = 12
ANSWER:A
Answer: A
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Options:
A)10.30 a.m.
B)10.00 a.m.
C)9.30 a.m.
D)9.00 a.m.
E)9.45 a.m.
Rationale: Explanation:
D = 110 â€“ 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
ANSWER IS B
Answer: B
Question: After decreasing 80% in the price of an article costs Rs.320. Find the actual cost of an article?
Options:
A)2777
B)2987
C)1200
D)9977
E)1600
Rationale: CP* (20/100) = 320
CP= 16* 100 => CP = 1600
Answer: E
Answer: E
Question: After M students took a test, the average score was 74%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 75%?
Options:
A)0.5M + 37
B)M + 0.74
C)0.75M - 0.5
D)0.5M + 37.5
E)37-0.5M
Rationale: The total number of correct answers for M students is (0.74)*50*M=37*M
For an average of 75%: (total correct answers) / (M+1) = 0.75*50=37.5
Let x be the number of correct answers for the next student.
(x + 37M) / M+1 = 37.5
x + 37M= 37.5M+37.5
x = 0.5M + 37.5
The answer is D.
Answer: D
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in?
Options:
A)12 1/2 days
B)12 1/8 days
C)12 6/2 days
D)16 1/2 days
E)12 2/2 days
Rationale: 15/25 + 10/x = 1 => x = 25
1/25 + 1/25 = 2/25
25/2 = 12 1/2 days
Answer: A
Answer: A
Question: A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability Q that both will be juniors?
Options:
A)1/10
B)1/5
C)2/9
D)2/5
E)1/2
Rationale: I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.
2 seniors = P(Senior) * P(Senior) = 2/9
1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9
Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability Q that it is two juniors is 1- (7/9) = 2/9.C
Answer: C
Question: A certain chocolate bar manufacturer reduced the weight of Chocolate Bar M by 20 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of chocolate Bar M?
Options:
A)20
B)24
C)25
D)28
E)30
Rationale: assume 1oz candy cost $1 before.
now price remain same $1 but weight of candy reduces to 0.8 oz
new price of candy = 1/0.8 =1.25
price increase 25 %
C
Answer: C
Question: A works twice as fast as B.If B can complete a work in 12 days independently,the number of days in which A and B can together finish the work is :
Options:
A)4 days
B)6 days
C)8 days
D)18 days
E)None of these
Rationale: Solution
Rates of worktio of raing of A and B = 2: 1.So, ratio of times taken = 1: 2
∴ A’s 1 day’s work = 1/6 B’s 1 day’s work =1/12
(A + B)'s 1 day’s work =(1/6 + 1/12)= 3/12=1/4
So,A and B together can finish the work in 4 days.
Answer A
Answer: A
Question: The total of the ages of Amar, Akbar and Anthony is 66 years. What was the total of their ages four years ago ?
Options:
A)71
B)44
C)54
D)16
E)18
Rationale: Explanation:
Required sum = (66 - 3 x 4) years = (66 - 12) years = 54 years.
Answer: C
Answer: C
Question: what is rate of interest if principal.amount be 400,simple interest 100 and time 2year.
Options:
A)10
B)12.5
C)25
D)12
E)14.5
Rationale: s.i=(p*r*t)/100
100=800r/100
r=100/8=12.5%
answer B
Answer: B
Question: A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be purple?
Options:
A)15%
B)20%
C)25%
D)43%
E)52%
Rationale: p = 26 , g=15 , y=9
total = 50
p(purple)=(26/50)*100 = 52% . Ans = E
Answer: E
Question: If x and y are positive integers, Choose which of the following CANNOT be the greatest common divisor of 15x and 20y?
Options:
A)5
B)5(x-y)
C)20x
D)20y
E)35x
Rationale: We are looking for a choice that CANNOT be the greatest common divisor of 15x and 20y ...which means 15x and 20y when divided by the answer choice the quotient should not be a integer.
lets check
a. 5 15x/5 = 3x and 20y/5 = 4y both are integers so eliminate
b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate
c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 35x and 20y ...
or 15x/20x = 3/4 which is not a integer.
so answer is C.
Answer: C
Question: If (x/y)=(6/5), find the value (x^2+y^2)/(x^2-y^2)
Options:
A)61/11
B)59/11
C)51/77
D)41/11
E)None of them
Rationale: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(6/5)^2+1] / [(6/5)^2-1]
= [(36/25)+1] / [(36/25)-1] = (61*25)/(25*11) = 61/11
Answer is A.
Answer: A
Question: Q:Robert purchased $1500 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
Options:
A)10
B)20
C)27
D)30
E)40
Rationale: I started off with looking at the answer choices... 10-20-27-30 are in a tight range, so my guess was to look and rule out the bigger numbers.
The total amount is $1500. So with 40 bonds, each $50 = $2000 , we already exceed the $1500 limit. Hence E is the answer.
Answer: E
Question: The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
Options:
A)1008
B)1015
C)1022
D)1032
E)None
Rationale: Solution
Required numbers	=(L.C.M of 12,16,18,21,28) + 7
‹=›1008 + 7
= 1015.
Answer B
Answer: B
Question: There are 12 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played?
Options:
A)55
B)66
C)77
D)88
E)99
Rationale: 12C2 = 66
The answer is B.
Answer: B
Question: Difference between the length &breadth of a rectangle is 26 m. If its perimeter is 208 m, then the ratio of area and perimeter is?? We have: (l - b) = 26 and 2(l + b) = 208 or (l + b) = 104?
Options:
A)315:26
B)315:25
C)315:30
D)415:35
E)425:35
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2 The required ratio is 2520 :208 =315 :26
A
Answer: A
Question: Miraa is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Miraa must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
Options:
A)75
B)150
C)3000
D)600
E)7,500
Rationale: I'd use backsolving for this question.
Check C:
3000 lenses = 1500 usable lenses = 750 tubes = 750 eyepieces. We CAN buy 750 tubes and 750 eyepieces, so that not to have leftovers.
Answer: C.
Answer: C
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Options:
A)No profit, no loss
B)5%
C)8%
D)10%
E)11%
Rationale: Explanation:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =80/100X100%=5%
ANSWER IS B
Answer: B
Question: The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.79 per square foot and 270 square feet of Zelzea Blue sod at $1.38 per square foot. What was the approximate average price per square foot paid for all the sod?
Options:
A)$1.63
B)$1.64
C)$1.66
D)$1.72
E)$1.76
Rationale: Average price = (550*1.79)+(270*1.38)/550+270=1.66 (Approx)
Answer C
Answer: C
Question: find value for x from below equation? x + 1 = 4
Options:
A)-5
B)-4
C)4
D)3
E)2
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = 4 - 1
2. Simplify both sides:
x = 3
D
Answer: D
Question: Today my car meter reads as 72527 kms. I notes that this is a palindrome. How many minimum kms i need to travel so my car meter find another palindrom.
Options:
A)100 kms
B)115 kms
C)110 kms
D)210 kms
E)100 kms
Rationale: E
100 kms
72527+100 = 72627 , a palindrome
Answer: E
Question: Working alone at its constant rate, pump M pumped out ¼ of the water in a tank in 2 hours. Then pumps N and O started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump N, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump O, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
Options:
A)6
B)12
C)15
D)18
E)24
Rationale: Rate of pump M = 1/8
3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4
Rate of M + Rate of N + Rate of O = 1/4
Rate of N + Rate of O = 1/4 - 1/8 = 1/8
N takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.
Rate of N = 1/24
1/24 + Rate of O = 1/8
Rate of O = 1/8 - 1/24 = 1/12
Time required to pump out all the water by O = 12 hrs
Answer: B
Answer: B