divelab/Sys2Bench huggingface dataset:
Question: How many factors of 990 are odd numbers greater than 1?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: When factorized, 990 has 5 prime factors. Of these prime factors 4 are odd and 1 is even. Hence total number of odd factors is 2*2*2*2(16), which includes 1. The total number of odd factors greater than 1 are 15.(option C)
Answer: C
Question: A sum of Rs.1420 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls
Options:
A)8B, 5G
B)5B, 8G
C)4B, 9G
D)9B, 4G
E)6B, 7G
Rationale: 120B+100G=1420-----i
B+G=13-------ii
from i
100B+20B+100G=1420
100(B+G)+20B=1420
100(13)+20B=1420
By simplifing we get
B=6;G=7
ANSWER:E
Answer: E
Question: For some integer p, p^2 - 5 is divisible by all of the following EXCEPT
Options:
A)30
B)38
C)41
D)29
E)31
Rationale: Hint: p^2-5 (p is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: A
Answer: A
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1200 per sq. metre.
Options:
A)Rs. 15000
B)Rs. 15550
C)Rs. 24750
D)Rs. 16500
E)None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1200 × 20.625) = 24750. Answer C
Answer: C
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr
Options:
A)25 Seconds
B)28 Seconds
C)30 Seconds
D)35 Seconds
E)40 Seconds
Rationale: Explanation:
Relative Speed = 63-3 = 60 Km/hr
= 60 *(5/18) = 50/3 m/sec
Time taken to pass the man will be
500âˆ—3/50=30seconds
ANSWER IS C
Answer: C
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
Options:
A)16
B)4
C)11
D)12
E)13
Rationale: d^2 = 12^2+4^2+3^2
d^2 = 122 + 42 + 32 = 13
Answer: E
Answer: E
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?
Options:
A)12
B)29
C)27
D)15
E)99
Rationale: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 105
6x + 15 = 105
6x = 90
x = 15
ANSWER:D
Answer: D
Question: The Present worth of Rs.2310 due years hence ,the rate of interest being 15% per annum, is :
Options:
A)Rs.1440
B)Rs.1750
C)Rs.1680
D)Rs.1840
E)None of these
Rationale: Explanation:
P.W.=Rs.[100×2310/100+(15×52)]=Rs.1680.
Answer: C
Answer: C
Question: All even numbers from 2 to 98 inclusive, except those ending in 0, are multiplied together what is the rightmost digit (the units digit) of the product?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: first multifly all numbers ending with 2 those are 2*12*22*32*42.......*92=2^10=4 is last digit
multify all numbers ending with 4=4^10=6 last digit
multify all numbers ending with 6=6^10= 6 last digit
multifly all numbers ending with 8=8^10=4 last digit
so 4*6*6*4=6 last digit
ANSWER:D
Answer: D
Question: A basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?
Options:
A)1/5
B)3/10
C)2/5
D)1/2
E)3/5
Rationale: Direct probability approach:
P=15∗44+45∗14=25P=15∗44+45∗14=25: probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}.
Reverse probability approach:
Again 1- the probability of the opposite event --> P=1−45∗34=25P=1−45∗34=25.
Answer: C
Answer: C
Question: What is the units digit of 29! + 50! + 3! + 3!?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: For all N greater than 4, the units digit of N! is 0.
The sum of the four units digits is 0 + 0 + 6 + 6 = 12
The units digit is 2.
The answer is B.
Answer: B
Question: If the milk and water ware added in the ratio 5:4 then how much more water should be added so he gets the ratio of 6:7.
Options:
A)11/6
B)11/7
C)11/8
D)6/11
E)7/11
Rationale: let quantity of water should added be x then
A/Q
5/(4+x)= 6/7
=> 35=24+6x
=> x=11/6
ANSWER:A
Answer: A
Question: if 5 tomatoes are worth 8 oranges,5 oranges are worth 4 apples, 7 apples are worth 3 pineapples and 7 pineapples cost rs.203,then he approx price of each tomato is
Options:
A)16
B)5
C)19
D)20
E)none of these
Rationale: 7 pineapples cost rs.203 means one pineapple cost is 29
7 apples are worth 3 pineapples means 7 apple cost 29*3. 1 Apple cost (29*3)/7
5 oranges are worth 4 apples. 1 orange cost is (29*3*4)/(7*5)
5 tomatoes are worth 8 oranges. 1 tomato cost is (29*3*4*8)/(7*5*5) = 2784/175 = 15.9
ANSWER:A
Answer: A
Question: A school’s annual budget for the purchase of student computers increased by 60% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
Options:
A)33.33%
B)40%
C)42%
D)48%
E)60%
Rationale: If last year, the budget was B and the price of one computer was P, then B/P was the number of purchased computers.
This year, 1.6B/(1.2P) = 4/3(B/P) = 1.33(B/P) computers can be purchased, which is 33.33% greater than the number of computers purchased last year.
Answer A.
Answer: A
Question: An unbiased cubic die is thrown.What is the probabiltiy of getting a multiple of 3 or 4?
Options:
A)1/9
B)1/12
C)1/2
D)3/4
E)3/8
Rationale: Explanation :
Total numbers in a die=6P(mutliple of 3) = 2/6 = 1/3P(multiple of 4) = 1/6P(multiple of 3 or 4) = 1/3 + 1/6 = 1/2
Answer : C
Answer: C
Question: In a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both?
Options:
A)132
B)26
C)17
D)11
E)12
Rationale: Explanation:Total pupil = 55
Debate + Singing = 10 + 18 = 28
The intersection for two = 55 â€“ 10 â€“ 28 = 17 play both games.
Answer: C
Answer: C
Question: Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
Options:
A)9.20 a.m
B)9.25 a.m
C)9.35 a.m
D)10.05 a.m
E)None of these
Rationale: Explanation:
Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
ANSWER IS E
Answer: E
Question: If point A coordinates are (-6, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.
Options:
A)(-2, - 2/3)
B)(2, -2/3)
C)(2/3, -2)
D)(0, 2)
E)(2, 2/3)
Rationale: Look at the diagram below:
Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-6+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be B.
Answer: B.
Answer: B
Question: Of the 420 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
Options:
A)200 to 260
B)160 to 260
C)220 to 260
D)220 to 300
E)40 to 100
Rationale: W=260
P=300
ALL=420
N(NEITHER)=AT LEAST 60
BOTH=?
W+P-BOTH+N=ALL
260+300-BOTH+60=420
BOTH=200
now pay attention to the fact, that both at most can be 260, since W=260
so, the answer is A
Answer: A
Question: A seller of used cars has 10 cars to sell and each of his clients selected 2 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?
Options:
A)8
B)10
C)15
D)14
E)16
Rationale: IfNo caris selected more than once then the number of clients = 10/2 =5
But since every car is being selected three times so No. of Clients must be thrice as well =5*3 = 15
Answer: option C
Answer: C
Question: A man sells a car to his friend at 13% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
Options:
A)Rs.21724.14
B)Rs.31724.14
C)Rs.51724.14
D)Rs.61724.14
E)None of these
Rationale: Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120Ã—54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 13%.
Now S.P = Rs.45000 and loss = 13%
C.P. Rs.[100/87Ã—45000]= Rs.51724.14.
Correct Option : C
Answer: C
Question: Three people each took 6 tests. If the ranges of their scores in the 6 practice tests were 17, 28 and 35, 42 what is the minimum possible range in scores of the three test-takers?
Options:
A)a 17
B)b) 28
C)c) 35
D)d) 45
E)e) 80
Rationale: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
C- 0 and 35
D-0 and 42
therefore the minimum range is 42, it cant be any lower however you play with the numbers.
D
Answer: D
Question: A room 5.44m long and 3.74m broad is to be paved with square tiles. The least number of square tiles required to cover the floor is:
Options:
A)176
B)192
C)184
D)162
E)172
Rationale: Area of the room= 544*374 sq.cm
Size of largest square tile= HCF of 544 cm & 374cm
Area of 1 tile= 34*34 sq.cm
Therefore, number of tiles= (544*374/34*34)= 176
ANSWER:A
Answer: A
Question: A textile manufacturing firm employees 125 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 125 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
Options:
A)13000
B)7000
C)10000
D)2800
E)None of these
Rationale: Explanation :
Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000Ã—(124/125)âˆ’150000Ã—(124/125)âˆ’75000.
=>Rs 2,72,200.
Decrease in profit
=>2,75,000âˆ’2,72,200
=>Rs. 2,800.
Answer : D
Answer: D
Question: P, Q and R started a business by investing Rs.120000, Rs.135000 and Rs.150000 respectively. Find the share of each, out of the annual profit of Rs.56700.
Options:
A)17850, 18900, 21000
B)16800, 18900, 21000
C)17850, 18900, 22000
D)18900, 17850, 21000
E)21000, 18900, 17850
Rationale: P : Q : R = 120000:135000:150000
=120:135:150=24:27:30=8:9:10
Share of P
=56700×8/27=2100×8=16800
Share of Q
=56700×9/27=2100×9=18900
Share of R
=56700×10/27=2100×10=21000
Answer is B.
Answer: B
Question: In a class of 40 students, 5 students did not borrow any books from the library, 15 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?
Options:
A)3
B)5
C)8
D)13
E)18
Rationale: The average number of books per student was 2means that total of 2*40=80 books were borrowed;
5+15+10=30 students borrowed total of 5*0+15*1+10*2=35 books;
So 80-35=45 books are left to distribute among 40-30=10 students, these 10 arethe rest who borrowed at least 3 books;
Tomaximizethe number of books one student from above 10 could have borrowed we shouldminimizethe number of books other 9 students from 10 could have borrowed. Minimum these 9 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 9*3=27 books. So the 10th student could have borrowed is 45-27=18 books.
Answer: E.
Answer: E
Question: What least number must be subtracted from 427398 so that remaining no.is divisible by 14
Options:
A)3
B)5
C)6
D)7
E)8
Rationale: Explanation:
On dividing 427398 by 14 we get the remainder 6, so 6 should be subtracted
Answer: Option C
Answer: C
Question: If the perimeter of a rectangular stadium is 800 m, its length when its breadth is 300 m is?
Options:
A)500
B)400
C)300
D)200
E)100
Rationale: 2(l + 300) = 800 => l = 100 m Answer: E
Answer: E
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)28
B)27
C)16
D)29
E)24
Rationale: 10 * 15 + 36 – 26
= 160/10
= 16
Answer:C
Answer: C
Question: The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 18,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?
Options:
A)5,476,811 kilometers squared
B)8,500,148 kilometers squared
C)9,843,123 kilometers squared
D)1,878,965 kilometers squared
E)4,787,900 kilometers squared
Rationale: he difference between the areas of Russia and China is given by
18,098,242 - 9,598,094 = 8,500,148 kilometers squared
correct answer B
Answer: B
Question: On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
Options:
A)5
B)50
C)10^5
D)5^10
E)8^10 - 3^10
Rationale: For n=3, consider the intensity to be x.
For n+1 = 4 , we have [intensity*10 ]= 10x
For n+2 = 5 , we have [10x*10 ]= 100x
For n+3 = 6 , we have [100x*10 ]= 1000x
For n+4 = 7 , we have [1000x*10 ]= 10000x
For n+5 = 8 , we have [10000x*10 ]= 100000x
Now , for n = 8 -->100000x = 10^5 x
which is 10^5 times x, the original intensity at n=3
ANSWER:C
Answer: C
Question: If it takes a tub 4 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?
Options:
A)48 seconds
B)1 minute, 12 seconds
C)1 minute, 36 seconds
D)2 minutes, 14 seconds
E)4 minutes, 12 seconds
Rationale: If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.
If it takes 4 minutes to drain 5/7 th of tub it takes 4*(7/5) minutes to drain the entire tub and 4*(7/5)*(2/7) min to drain 2/7 th of the tub which is 8/5 minutes or 1 3/5 minutes or 1 minute 36 seconds
So answer is C
Answer: C
Question: if none of the figures 2,4,5,7,8,0 be repeated,how many different numbers of 4 digits can be formed wiyh them.?
Options:
A)150
B)200
C)250
D)300
E)350
Rationale: here 1st place can be filled by five ways(i.e any one from 2,4,5,7,8),and second place will be again in 5 ways (remaining from 6 digits ,6-1=5) and next place in 4 ways ,and again in 3 ways so ans will be 5*5*4*3=300
ANSWER:D
Answer: D
Question: Find the least multiple of 23,which when divided by 18,21 and 24 leaves remainders 7,10 and 13 respectively.
Options:
A)3002
B)3013
C)3024
D)3036
E)None of these
Rationale: Solution
Here (18 - 7) = 11, (21 - 10) = 11 and (24 - 13) = 11. L.C.M. of 18,21 and 24 is 504.
Let required number be 504 k - 11.
Least value of k for which (504 k - 11 ) is divisible 23 is k = 6.
So, Required number = 504 × 6 - 11 =3024 - 11 = 3013.
Answer B
Answer: B
Question: In how many ways can the letters of the word AGENDA be rearranged such that the vowels always appear together?
Options:
A)6!/2!
B)3!*3!
C)4!/2!
D)(4! *3!)/2!
E)3!*3!/2
Rationale: In the word ABACUS , there are 3 vowels - 2 A's and E
Number of ways the letters of word AGENDA be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Answer: D
Question: At a kennel with 80 dogs, 45 of the dogs wear tags and 40 wear flea collars. If 6 of the dogs wear both, then how many of the dogs wear neither a collar nor tags?
Options:
A)1
B)6
C)34
D)79
E)85
Rationale: Dogs wear neither a collar nor tags = 80 - ( 45 + 40 - 6 )
Dogs wear neither a collar nor tags = 80 - 79
Dogs wear neither a collar nor tags = 80 - 79
Hence, answer will be 1
ANSWER:A
Answer: A
Question: The difference between a two-digit number and the number after interchanging the position of the two digits is 36. What is the difference between the two digits of the number?
Options:
A)4
B)6
C)3
D)Cannot be determined
E)None of these
Rationale: Let the two-digit no. be l0x + y.
Then, (10x + y) – (10y + x) = 36
or, 9(x – y) = 36
or, x – y = 4
Answer A
Answer: A
Question: 3 litre of water is added to 11 litre of a solution containing 42% of alcohol in the water. The percentage of alcohol in the new mixture is?
Options:
A)30%
B)33%
C)35%
D)40%
E)45%
Rationale: We have a 11 litre solution containing 42% of alcohol in the water.
=> Quantity of alcohol in the solution
=
11
×
42
100
=11×42100
Now 3 litre of water is added to the solution.
=> Total quantity of the new solution = 11 + 3 = 14
Percentage of alcohol in the new solution
=
11
×
42
100
14
×
100
=11×4210014×100
=
11
×
3
100
=
33%
B)
Answer: B
Question: The population of a town is 10000. It increases annually at the rate of 27% p.a. What will be its population after 2 years?
Options:
A)14000
B)14400
C)16129
D)14600
E)14700
Rationale: Formula :
10000 × 127/100 × 127/100 = 16129
Answer : C
Answer: C
Question: Find the no of ways in which 6 toffees can be distributed over 5 different people namely A,B,C,D,E.
Options:
A)210
B)211
C)212
D)213
E)214
Rationale: acc to formula (n+r-1)C (r-1) = (6+5-1)C(5-1)
=10C4 = 210
ANSWER:A
Answer: A
Question: The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $6.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
Options:
A)$4.50
B)$5.10
C)$5.30
D)$5.50
E)$6.50
Rationale: I Tried using Time/Rate approach:-
Initial Price Difference = 6.80 - 3.20 = 3.60
Price of Corn increasing by 5x
Price of Wheat decreasing by x(1.4)-x = .4x
Since both the quantities are moving towards reducing the Price Gap hence:-
Relative Increase = 5x +.4x
Let T be the Time by which GAP is filled so,
3.6 = T(5.4x) -> T= (3.6)/5.4X
Final Price = 3.20 + 5X * T -> 3.20 + 5*3.6/5.4 = 6.5
Answer E.
Answer: E
Question: The three competitors in a race have to be randomly chosen from a group of four men and three women. How many different such trios contain at least one woman?
Options:
A)10
B)15
C)16
D)31
E)46
Rationale: The total number of ways to choose three runners 7C3 = 35
The number of trios with only males is 4C3 = 4
The number of trios which include at least one woman is 31.
The answer is D.
Answer: D
Question: Four percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
Options:
A)15%
B)20%
C)25%
D)60%
E)72%
Rationale: Initially 96% and 4% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗96
so, the required % is [(3/4)∗96/100]∗100 = 72%
ANSWER:E
Answer: E
Question: There are three guys who have equal number of bullets. All of them shoot 12 bullets. The remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division. What was the original number of bullets each one had?
Options:
A)18
B)19
C)30
D)45
E)54
Rationale: let initially each was having x bullets
they shot 12 bullets
so 3x-36=x
x=18
so each was having 18 bullets.
total was 54.
ANSWER:E
Answer: E
Question: What is the sum of all four digit integers formed using the digits 3 ,4 ,5 and 6 (repetition is allowed)
Options:
A)1279874
B)1279872
C)1279875
D)1279876
E)1279870
Rationale: n = 4 * 4 * 4 * 4 = 256
<x> = (6666 + 3333) / 2 = 4999.5
Sum = number of integers x average value
n * <x> = 256 * 4999.5 = 1279872
answer = B
Answer: B
Question: Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers?
Options:
A)015
B)28
C)17
D)19
E)11
Rationale: Explanation:
x + y = 80
x â€“ 4y = 5
x = 65 y = 15
Answer:A
Answer: A
Question: Y invested $1000 in a business and Z invested $3000 in a business. At the end of the year they got $4000 as the profit. Find their share?
Options:
A)$1000,$2000
B)$2000,$3000
C)$1000,$3000
D)$2000,$3000
E)$3000,$4000
Rationale: Y:Z = 1000:3000
Y:Z = 1:3
Y's share = 4000*1/4 = $1000
Z's share = 4000*3/4 = $3000
Answer is C
Answer: C
Question: If the price of petrol increases by 25% and Bill intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
Options:
A)A)8%
B)B)7%
C)C)10%
D)D)6%
E)E)9%
Rationale: Explanation:
Assume that the initial price of 1 Litre petrol = Rs.100 ,Bill spends Rs.100 for petrol,
such that Bill buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Bill spends additional 15% on petrol,
amount spent by Bill = 100× (100+15)/100 = Rs.115
Hence Quantity of petrol that he can purchase = 115/125 Litre
Quantity of petrol reduced = (1−115/125) Litre
Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8%
Answer: Option A
Answer: A
Question: A person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is?
Options:
A)1266
B)2887
C)2668
D)1200
E)1765
Rationale: Let the parts be x, y and [2600 - (x + y)].
Then,
(x * 4 * 1)/100 = (y * 6 * 1)/100 = {[2600 - (x + y)] * 8 * 1}/100
y/x = 4/6 = 2/3 or y = 2/3 x
So, (x * 4 * 1)/100 = [(2600 - 5/3 x) * 80/100
52x = (7800 * 8) => x = 1200
Money invested at 4% = Rs. 1200.
Answer:D
Answer: D
Question: What is the difference between the place value of 2 in the numeral 7889?
Options:
A)160
B)165
C)180
D)190
E)720
Rationale: Answer: Option 'E'
800 - 80 = 720
Answer: E
Question: If two balls are randomly selected from a green urn containing 7 black and 7 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?
Options:
A)A.2/9
B)B.4/9
C)C.3/13
D)D.1/3
E)E.1/9
Rationale: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.
Probability (first ball is white) = 7/14
Probability(second ball is white) = 6/13
Probability (both balls are white) = (7/14)*(6/13) = 3/13
Answer C
Answer: C
Question: What is the probability of rolling a total of 4 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
Options:
A)1/12
B)1/6
C)2/7
D)1/3
E)1/2
Rationale: Totalsample spacefrom two fair six-sided dice is 36.
There are six possible ways to be 7 i.e. (1+3), (2+2), (3+1)
So, total probability is 3/36 or 1/12.
Answer is A.
Answer: A
Question: The age of man is three times the sum of the ages of his two sons. Six years hence,his age will be double of the sum of the ages of his sons.The fatherâ€™s present age is :
Options:
A)40 years
B)45 years
C)50 years
D)54 years
E)75 years
Rationale: Solution
Let the sum of present ages of the two sons be x years.
Then,father's present age = 3x years.
âˆ´ (3x + 6)=2 (x +12) â‡” 3x + 6 = 2x + 24â‡” x =18.
Hence,father's present age = 54 years. Answer D
Answer: D
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
Options:
A)20
B)21
C)22
D)28
E)NONE
Rationale: Sol.
Let the total number of workers be x. Then,
8000x = (14000 × 7) + 6000 ( x – 7)
‹=› 2000x = 56000
‹=› x = 28.
Answer D
Answer: D