divelab/Sys2Bench huggingface dataset:
Question: What is the largest 4 digit number exactly divisible by 12?
Options:
A)4676
B)4678
C)8888
D)9504
E)9996
Rationale: Largest 4 digit number = 9999
9999 ÷ 12 = 833, remainder = 3
Hence largest 4 digit number exactly divisible by 12
= 9999 - 3 = 9996
answer :E
Answer: E
Question: There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 14 have taken a course in finance and 15 have taken a marketing course. 10 of the employees have taken exactly two of the courses and 1 employee has taken all three of the courses. How many of the 50 employees have taken none of the courses?
Options:
A)11
B)5
C)9
D)8
E)10
Rationale: 50 Employees. Counting every different attendand to the courses we have:
Accounting: 22
Finance: 14
Marketing: 15
Which would add up to 51 different attendands, which is not possible.
Now 10 have taken exactly 2 courses, which means that there are 10 less different attendands. Say that 10 of the Finance attentands also attended Accounting.
51-10= 41
1 Person has taken all three courses. As above, we subtract him from the number of different attendands. Since this time the person took all three courses, we have to substract him two times.
41-2= 39.
Answer : A
Answer: A
Question: A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 35% impurities to the product. Find the net profit percentage of the dealer?
Options:
A)44%
B)40%
C)68.75%
D)56.25%
E)36%
Rationale: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.
It means that he is selling $4 worth of product for $5.
The dealer then further added 35% impurities to the product.
It means that he is selling $5 worth of product for $6.75.
So his profit is $6.75-$4 = $2
and his profit percent is
(2.75/4)*100 = 68.75%
Answer:- C
Answer: C
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 28150. What percentage of profit did he make?
Options:
A)22
B)27
C)40
D)26.5
E)11
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 28150
Profit(%) = (28150 - 22250)/22250 * 100 = 26.5%.Answer:D
Answer: D
Question: A circular swimming pool is surrounded by a concrete wall 4 feet wide.if the area of the wall is 11/25 of the area of the pool, then the radius of the pool in feet is?
Options:
A)22
B)20
C)9
D)8
E)1
Rationale: Let the radius of the pool be r. Then area of the wall and pool = π(r+4)2π(r+4)2
Area of the pool = π(r)2π(r)2
Area of the wall = π(r+4)2−π(r)2π(r+4)2−π(r)2
Given π(r+4)2−π(r)2π(r+4)2−π(r)2 = 1125(πr2)1125(πr2)
r2+8r+16−r2=1125r2r2+8r+16−r2=1125r2
11r2−200r−400=011r2−200r−400=0
Solving r = 20
Answer:B
Answer: B
Question: Rs.200 amounts to Rs.800 in 8 years at simple interest. If the interest is increased by 5%, it would amount to how much?
Options:
A)520
B)440
C)260
D)280
E)120
Rationale: (200*5*8)/100 =80
200+ 80 = 280
Answer: D
Answer: D
Question: A driver would have reduced the time it took to drive from home to the store by 1/4 if the average speed had been increased by 10 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?
Options:
A)12
B)15
C)20
D)25
E)30
Rationale: Since the distance remains the same (we're just changing the rate and time), any increase in rate or time is met with a decrease in the other term. Decreasing the time by 1/4 would give us:
D = (R)(T) = (3T/4)(x*R)
x = 4/3 since (3T/4)(4R/3) = (R)(T) = D
4R/3 = R + 10
R/3 = 10
R= 30
The answer is E.
Answer: E
Question: An investment of d dollars at k percent simple annual interest yields $900 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $1,800 over a 3 year period?
Options:
A)(2d)/3
B)(3d)/4
C)(4d)/3
D)(3d)/2
E)(8d)/3
Rationale: 900 dollars in 2 years means 450 dollars in 1 year.
To get 1800 dollars' it will take 4 years.
To get 1800 in 3 years, we need 4/3 times money. Answer is C.
Answer: C
Question: Find the sum of all the four digit numbers which are formed by digits 1, 2, 5, 6
A.
B.
C.
D.
Options:
A)933510
B)93324
C)65120
D)8400
E)7400
Rationale: There are 4!=24 four digit numbers which are formed by digits 1, 2, 5, 6.
Obviously 24/4=6 numbers will end with 1; 6 numbers will end with 2, 6 numbers with 5 and 6 numbers with 6.
6*1+6*2+6*5+6*6=6*14=84, which means that the sum of all these 24 numbers must end by 4, only answer choice with 4 at the end is B.
Answer: B.
Answer: B
Question: How many 2 digit number satisfy the following. that last digit of the square of the 2 digit number is 8 ?
Options:
A)1
B)2
C)3
D)More than three
E)None
Rationale: as no perfect square is having last digit as 8.
ANSWER:E
Answer: E
Question: What is the area of a square field whose sides have a length of 14 meters?
Options:
A)196 sq m
B)286 sq m
C)298 sq m
D)267 sq m
E)231 sq m
Rationale: 14 * 14 = 196 sq m
The answer is A.
Answer: A
Question: Here is a list of names with numbers assigned to them
Lavesh = 622
Anmol = 522
Shruti = 620
Aakriti = 742
Based on above Logic what is the value of Sonal ?
Options:
A)522
B)422
C)624
D)570
E)750
Rationale: A
1st Number = Number of alphabtes
2nd Number = Number of vowels
3rd Nummber = Number Of Circles
Lavesh = 6 alphabets + 2 vowels(a,e) + 2 circles(in 'a' and in 'e') = 622
Anmol = 5 alphabets + 2 vowels(a,0) + 2 circles(in 'a' and in 'e') = 522
Shruti = 6 alphabets + 2 vowels(u,i) + 0 circles = 620
Aakriti = 7 alphabets + 4 vowels(a,a,i,i) + 2 circles(in 'A' and in 'a') = 742
Hence,
Sonal = 5 alphabets + 2 vowels(a,o) + 2 circles(in 'a' and in 'o') = 522
Answer: A
Question: If (x - 1)^2 = 361, which of the following could be the value of x - 5?
Options:
A)16
B)14
C)-23
D)-25
E)-26
Rationale: (x - 1)^2 = 361
(x - 1) = 19 or -19
x = 20 or -18
x - 5 = 15 or -23
The answer is C.
Answer: C
Question: There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 54%
Options:
A)18.75
B)19.75
C)20.75
D)33
E)22.75
Rationale: 60*84/100=50.40 lit milk that is 9.60 lit water
let x lit water will be added then
(60+x)*54/100=50.40
so x=33.33
ANSWER:D
Answer: D
Question: In an IT company, there are a total of 60 employees including 50 programmers. The number of male employees is 80, including 35 male programmers. How many employees must be selected to guaranty that we have 3 programmers of the same sex?
Options:
A)15
B)50
C)55
D)35
E)65
Rationale: You could pick 10 non-programmers, 2 male programmers, and 2 female programmers, and still not have 3 programmers of the same sex. But if you pick one more person, you must either pick a male or a female programmer, so the answer is 15.
A
Answer: A
Question: How many number of 3's would be used to type numbers from 1 to 700
Options:
A)210
B)220
C)230
D)240
E)250
Rationale: 1-99--20 (3,13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93)
likewise
100-199--20
200-299--20
300-399--120 (300-399 there is extra 100 3's)
400--499--20
500--599--20
600-700--20
20+20+20+120+20+20+20=240
ANSWER:D
Answer: D
Question: A and B are working on an assignment. A takes 6 hours to type 32 pages on a computer, while B takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Options:
A)3 hours
B)8 hours
C)6 hours
D)7 hours
E)9 hours
Rationale: B
8 hours
Number of pages typed by A in one hour=32/6=16/3
Number of pages typed by B in one hour=40/5=8
Number of pages typed by both in one hour=((16/3)+8)=40/3
Time taken by both to type 110 pages=110*3/40=8 hours.
Answer: B
Question: If 144/x is an integer and 100/x is an integer, which of the following must be true?
I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer
Options:
A)I only
B)III only
C)I and II only
D)II and III only
E)I, II and III
Rationale: I think, here we should use the greatest common factor.
The greatest common factor for 144 and 108 is 36.
So 36/x is an integer.
For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions.
Ans is D.
Answer: D
Question: 1, 9, 25, 49, 81, ?
Options:
A)121
B)114
C)153
D)158
E)138
Rationale: A
121
The series consists of squares of consecutive prime numbers.
Answer: A
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 141, what is the difference between the ages of Patrick and Monica?
Options:
A)27
B)48
C)45
D)72
E)18
Rationale: Ages of P and Mi=3x+5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=47x=141
x=3
Difference if ages of Pa and Mo=25x-9x=16x=16*3=48
Answer B
Answer: B
Question: A $74.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?
Options:
A)15%
B)20%
C)25%
D)60%
E)80%
Rationale: Listed selling price of chair = 74.95 $
Discounted selling price of chair = 59.95 $
Discount = 74.95 - 59.95 = 15 $
% decrease in price of chair = (15/74.95) * 100% = 20 % approx
Answer B
Answer: B
Question: Linda spent 2/3 of her savings on furniture and the rest on a TV. If the TV cost her $250, what were her original savings?
Options:
A)$750
B)$350
C)$650
D)$550
E)$850
Rationale: If Linda spent 2/3 of her savings on furniture, the rest
3 / 3 - 2 / 3 = 1 / 3 on a TV
But the TV cost her $250. So 1 / 3 of her savings is $250. So her original savings are 3 times $250 = $750
correct answer A
Answer: A
Question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Options:
A)6
B)9
C)8
D)2
E)3
Rationale: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81
= 9
Answer:B
Answer: B
Question: What is the sum of the multiples of 6 from 48 to 72, inclusive?
Options:
A)500
B)600
C)700
D)300
E)400
Rationale: The formula we want to use in this type of problem is this:
Average*Total Numbers=Sum
First, find the average by taking the sum of the F + L number and divide it by 2:
A = (F + L)/2
Second, find the total numbers in our range by dividing our F and L numbers by 7 and add 1.
(72/6) - (48/6) + 1
Multiply these together so what we show Average*Total Numbers=Sum
(48 + 72)/2 * (72/6) - (48/6) + 1 = Sum
60 * 5 = 300
D
Answer: D
Question: A steel vessel has a base of length 60 cm and breadth 30 cm. Water is poured in the vessel. A cubical steel box having edge of 30 cm is immersed completely in the vessel. How much will the water rise?
Options:
A)7.5 cm rise
B)10 cm rise
C)15 cm rise
D)30 cm rise
E)None of these
Rationale: Explanation:
Volume of Cube=a3=a*a*a
60cm*30cm*H=30cm*30cm*30cm
H=15cm
ANSWER IS C
Answer: C
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person?
Options:
A)56 kg
B)80 kg
C)85 kg
D)Data inadequate
E)None of these
Rationale: B
80 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (60 + 20) kg = 80 kg.
Answer: B
Question: The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum T of all the digits of the integers from 0 to 99 inclusive?
Options:
A)450
B)810
C)900
D)1000
E)1100
Rationale: We want the sum of the digits from 0 to 99, so I approximated:
0-9 ->45-> (9+0)*10/2
40-49 ->85(13+4)*10/2
90-99 ->135(18+9)*10/2
We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just T=900:the answer is C.
Answer: C
Question: A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
Options:
A)1/20
B)1/12
C)1/5
D)4/21
E)5/21
Rationale: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 2*x
Hence, a1+a2+..+a20+n = 22x
So, the fraction asked = 2x/22x = 1/12
B
Answer: B
Question: if the ratio of two number is 2:5 and LCM of the number is 160 then what is the number.
Options:
A)15
B)20
C)16
D)30
E)35
Rationale: product of two no = lcm *hcf
2x*5x=160*x
x=16
ANSWER:C
Answer: C
Question: A CREAM manufacturer produces 200 units of a certain model each month at a cost to the manufacturer of £20 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £20,000?
Options:
A)100
B)110
C)1120
D)200
E)220
Rationale: 200(x-20)≥20,000
x-20≥200
x≥220
Answer: Option E
Answer: E
Question: A watch was sold at a loss of 9%. If it was sold for Rs.220 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)2876
C)1977
D)2778
E)1692
Rationale: 91%
104%
--------
13% ---- 220
100% ---- ? => Rs.1692
Answer: E
Answer: E
Question: How many 11-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12345654321.
Options:
A)100
B)610
C)729
D)900
E)900000
Rationale: Take the task of building palindromes and break it intostages.
Stage 1: Select the 11th digit
We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in9ways
Stage 2: Select the 10th 9th,8th, 7th, 6th digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in10ways
IMPORTANT: At this point, the remaining digits are alreadylocked in.
Stage 3: Select the , 5th, 4th, 3rd, 2nd, 1st digit
So, we can complete this stage in1way.
By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 11-digit palindrome) in(9)(10)(10)(10)(10)(10)(1)(1)(1)(1)(1)ways (= 900000 ways)
Answer: E
Answer: E
Question: A batsman scored 150 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)45(4/11) %
B)60 %
C)45(5/11) %
D)44(5/11) %
E)None of these
Rationale: Explanation :
Total runs scored = 150
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 150 - 60 = 90
Required % = (90/150) × 100 =60%
Answer : Option B
Answer: B
Question: The average monthly salary of 20 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
Options:
A)3700
B)3890
C)88798
D)2789
E)2891
Rationale: Explanation:
Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700.
Answer: A) 3700
Answer: A
Question: If k is an integer and 2 < k < 6, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: (6-2) < k < (6+2)
4 < k < 8
thus k = 5, 6, 7
Since 2 < k < 6, then k can be 5.
The answer is B.
Answer: B
Question: A fill pipe can fill 1/2 of cistern in 20 minutes. In how many minutes, it can fill 1/2 of the cistern?
Options:
A)5min
B)10min
C)15min
D)20min
E)25min
Rationale: Required time = 20*2*1/2 = 20 minutes
Answer is D
Answer: D
Question: A bag contains 4 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?
Options:
A)2/5
B)3/5
C)1/5
D)7/15
E)8/15
Rationale: Total number of balls = (4 + 5 + 6) = 15.
Therefore, n(S) = 15.
Let E1 = event of drawing a red ball.
and E2 = event of drawing a green ball.
Then, E1 n E2 = f.
P (E1 n E2) = P(E1) + P(E2) = (4/15 + 5/15) = 9/15 = 3/5.
ANSWER:B
Answer: B
Question: The number of permutations of the letters of the word 'BUBBLEGUM' is?
Options:
A)9!/(2!)2
B)9!/2!
C)9!/3! 2!
D)8!/3! 2!
E)9!/2! 1! 1! 1!
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'BUBBLEGUM' consists of 9 letters of which there are 3B's, 2U's, 1L, 1G and 1M.
Number of arrangements = 9!/3! 2!
Answer: C
Answer: C
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $112 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
Options:
A)6
B)7
C)8
D)12
E)15
Rationale: $112 = 20*$5 + 4*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 20, 17, 14,...,2 for a total of 7 combinations.
The answer is B.
Answer: B
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:9
B)3:4
C)3:2
D)3:1
E)3:5
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4
Answer:B
Answer: B
Question: A retailer sells 10 shirts. The first 3 he sells for $20,$22 and $25. If the retailer wishes to sell the 10 shirts for an overall average price of over $20, what must be the minimum average price of the remaining 7 shirts?
Options:
A)$14.00
B)$16.00
C)$17.00
D)$19.00
E)$23.00
Rationale: First 3 shirts are sold for $20,$22 and $25=$67.
To get average price of $20,total sale should be 10*$20=$200
So remaining 7 shirts to be sold for $200-$67=$133
Answer should be 133/7=$19.00 that is D
Answer: D
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 20 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 10% chocolate?
Options:
A)18
B)20
C)16
D)22
E)24
Rationale: First, you must find the total weight of the mixture given that 80% of it will be dough.
90%*Total = 36 => (9/10)Total=36=> Total=360/9 => Total=40 oz,
From there, you must find 10% of the total 40 oz of the mixture.
10%*Total => (1/10)(40)= 4 oz choclate used,
Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 20-4 = 16 oz chocolate left over.
Answer : C
Answer: C
Question: If 4 men can color 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
Options:
A)1 day
B)2 days
C)3 days
D)4 days
E)5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
A
Answer: A
Question: A certain no. when divided by 20 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Options:
A)3
B)4
C)6
D)8
E)9
Rationale: Explanation:
20 + 25 = 45/15 = 3 (Remainder)
A
Answer: A
Question: A box contains nine slips that are each labeled with one number: 1, 2, 3, 8, 13, 21, 34 and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box?
Options:
A)7/72
B)1/6
C)7/36
D)15/36
E)1/7
Rationale: Probability = No: of desired outcomes / Total No: of outcomes.
You are picking two slips out of 8 slips. So
Total No: of outcomes = 8C2 = 28
Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?
If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome.
(1,2) (8,13) (13,21) (21,34) . There are 4 such pairs. If the two numbers which I pick is from any of these 4 pairs, then I get my desired outcome.
So No: of desired outcomes = 4
Probability = 4/28=1/7
Answer :E
Answer: E
Question: Kim has 7 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 14 shoes, what is the probability that she will select 2 shoes of the same color?
Options:
A)1/13
B)1/15
C)11/9
D)1/10
E)1/25
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 14 shoes = 14/14 = 1
Probability of selecting the next shoe (out of 14 available) having the same color = 1/14 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/13=1/13.
A is the correct answer.
Answer: A
Question: A train 225 m in length crosses a telegraph post in 15 seconds. The speed of the train is?
Options:
A)37 kmph
B)34 kmph
C)32 kmph
D)38 kmph
E)76 kmph
Rationale: S = 225/25 * 18/5
= 32 kmph
Answer: C
Answer: C
Question: A trader owes a merchant $10000 due 1 year hence. The trader wants to settle the account after 2 months. If the rate of interest 12% per annum, how much cash should he pay?
Options:
A)$9090.90
B)$9010.90
C)$7090.90
D)$8090.90
E)$9000.90
Rationale: Required money	= P.W. of $10000 due 10 months hence
= $((10000*100) / 100+ (12*10/12) )
= $9090.90
ANSWER:A
Answer: A
Question: Which of these lines in the xy-plane does not contain any point with two negative coordinates?
Options:
A)y = 3x
B)y = x + 7
C)y = x^2 - 4
D)y = x^3 + 3x
E)y = x^6
Rationale: x^6 is 0 when x is 0 and positive for all other values of x.
The answer is E.
Answer: E
Question: Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.
So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes.
If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1.
The number of 10 pound boxes remains the same so we still have 4 of them.
To get a ratio of 1:1, the number of 20-pound boxes must be 4.
We need to remove 12 of the 20-pound boxes.
The answer is B.
Answer: B
Question: The cash realised on selling a 14% stock is Rs.104.25, brokerage being 1/4% is?
Options:
A)104
B)106
C)102
D)192
E)122
Rationale: Cash realised= Rs. (104.25 - 0.25)
= Rs. 104.
Answer: A
Answer: A
Question: The triplicate ratio of 2:5 is?
Options:
A)1:0
B)8:125
C)1:7
D)1:2
E)1:1
Rationale: 23: 53 = 8:125
Answer: B
Answer: B
Question: There are 2000 students in a school and among them 10 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
Options:
A)1
B)10
C)100
D)50
E)20
Rationale: 10% of 2000 gives 200. so 200 attends chess and 50% of 200 gives 100
so 100 enrolled for swimming
Answer: C
Answer: C
Question: If y is an integer, then y(y - 1)( y- k) must be evenly divisible by three when k is any of the following values EXCEPT
Options:
A)-4
B)-6
C)-1
D)2
E)5
Rationale: if we put k=-1 we get:
y(y-1)(y+1) rearrange:(y-1)y(y+1)
so it looks like a sequenc,
if we assume that y=2 and put number from the answer then we get:
(y – 1)y(y – k)
k=5 =1.2.-3
k=2 =1.2.0
k=-1 =1.2.3
k=-4 =1.2.6
but when we put
k=-6 =1.2.8 not satisfied
so,the answer is B
Answer: B
Question: The grocer ordered deliveries of apples on each weekday. The numbers of apples he ordered per day were 80, 30, 100, 90 and x. If the median apple delivery was 10 apples larger than the average (arithmetic mean) number of apples delivered, which of the following could be x?
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: Look at the options available
Value of x seems to 50 < = x < = 70
A. 50
B. 55
C. 60
D. 65
E. 70
So position of x is second
30 , x , 80 , 90 , 100
Median = 80
Median number of apples was 10 points higher than the average, so average = 70
30 + x + 80 + 90 + 100 = 350
x = 50 = Answer = A
Answer: A