RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
A.1/24
B.1/8
C.1/4
D.1 by 3
Answer: D.1 by 3
Explanation: The number of ways to put exactly one letter in the right envelope is not equal to 4C1. There are 4C1 ways to choose which letter goes in the right envelope, but you then need to work out how many ways the remaining letters can be placed in the wrong envelope. For the first of these three letters, there are 2 wrong envelopes you could choose. Now, you still have one letter left which has its matching envelope unused; you must put this letter in the wrong envelope, so you have only 1 choice for this letter, and finally for the last letter you have only 1 choice for where to put it. So you have 2*1*1 = 2 ways to assign the remaining letters incorrectly, which is why you need to multiply your answer by 2.
I posted a slightly different solution to BTG a while ago, which I'll paste here:
One letter goes in the right envelope. It doesn't matter which envelope this is- there are three envelopes left. 2/3 chance the next letter goes in the wrong envelope, 1/2 the next one does, and 100% the last one does- its envelope must have been used already.
(2/3)(1/2) = 1/3.
Slightly old post, but very interesting explanation...
Just would like to add my 2 cents:
For 1 letter to go in right envelope - probability = 1/4
For 2nd letter to go in wrong envelope - probability = 2/3
For 3rd letter to go in wrong envelope - probability = 1/2
For 4th letter to go in wrong envelope - probability = 1
Now, in the order this arrangement can be done:
C - Letter going into correct envelope
W - Letter going into wrong envelope
No#1. C - W - W - W
No#2. W - C - W - W
No#3. W - W - C - W
No#4. W - W - W - C
There are 4 ways, it can be done
So, probability of 1 letter going in correct envelope: 4* (1/4) * (2/3) * (1/2) * 1 =1/3 D
Question: a person has 12004 coins of silver. How much would he need to add so that he can distribute equally among his seven children in whole numbers?
A.1 coin
B.2 coins
C.3 coins
D.4 coins
Answer: A.1 coin
Explanation: He would need to add one coin more so 12005 is fully divisible by 7 and each would get 1715 coins. So the correct answer is A
Question: The average weight of a group of boys is 20 kg. After a boy of weight 36 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
A.12
B.15
C.18
D.24
Answer: B.15
Explanation: Let the number off boys in the group originally be x.
Total weight of the boys = 20x
After the boy weighing 36 kg joins the group, total weight of boys = 20x + 36
So 20x + 36 = 21(x + 1) = > x = 15
ANSWER:B
Question: A student can select one of 7 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.
A.22
B.84
C.99
D.37
Answer: B.84
Explanation: 7C1×3C1×4C1 = 7x3x4=84 ways
Answer:B
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
A.3/8
B.7/16
C.2/7
D.9/16
Answer: C.2/7
Explanation: P(getting prize)=10/(10+25)
=10/35
=2/7
Option:C
Question: A cistern 4m long and 2 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
A.23 m2
B.20 m2
C.52 m2
D.24 m2
Answer: A.23 m2
Explanation: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (2 x 1.25 + 4 x 1.25) + 4 x 2] m2
= 23 m2.
answer :A
Question: Of the three- digit integers greater than 700, how many have two digits E that are equal to each other and the remaining digit different from the other two?
A.90
B.82
C.80
D.45
Answer: C.80
Explanation: three-digit integers greater than 700: 701 to 999, inclusive.
possible values for hundreds-digit--> 7,8,9
possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9
when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999
when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999
when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700
E=27+27+26 = 80
Answer: C
Question: The number which exceeds 16% of it by 21 is :
A.25
B.52
C.58
D.60
Answer: A.25
Explanation: Solution
Solution
Let the number be x.
x-16% of x =21
x-16/100x =21
x-4/25x=21
21/25x=21
x=(21x25/21)= 25
Answer A
Question: If 5 < x < 11 and y = x + 7, what is the greatest possible integer value of x + y?
A.26
B.27
C.28
D.29
Answer: C.28
Explanation: x+y = x+x+7 = 2x+7
We need to maximize this value and it needs to be an integer.
2x is an integer when the decimal of x is .0 or .5
The largest such value is 10.5
Then x+y = 10.5 + 17.5 = 28.
The answer is C.
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
A.68 %
B.83.33%
C.59%
D.74.1%
Answer: C.59%
Explanation: Explanation:
Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.
Answer:C
Question: A person incurs a loss of 5% be selling a watch for Rs. 1140. At what price should the watch be sold to
earn 5% profit.
A.Rs.1200
B.Rs.1230
C.Rs.1260
D.Rs.1290
Answer: C.Rs.1260
Explanation: Explanation:
Let the new S.P. be x, then.
(100 - loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)
=>(951140=105x)=>x=1260
Answer: C
Question: What is the next number in the sequence : 10,11,13,17,25,32,37,47, __?
A.59
B.53
C.51
D.58
Answer: D.58
Explanation: next no. = previous + (sum of digits)
10 + (1+0) = 11
11 + (1+1) = 13
13 + (1+3) = 17
17 + (1+7) = 25
25 + (2+5) = 32
32 + (3+2) = 37
37 +(3+7) = 47
47 + (4+7) = 58
ANSWER:D
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
A.10000
B.2777
C.2657
D.2876
Answer: A.10000
Explanation: 100 * 100 = 10000
125 * 80 = 10000
No change
Answer: A
Question: John went to the Hospital at the speed of 60 km per hour while returning for his home he covered the half of the distance at the speed of 10 per hour, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest 1/2 of the distance at the speed of 30km per hour. The average speed of the John in the whole length of journey is?
A.16 km/hr
B.20 km/hr
C.24 km/hr
D.28 km/hr
Answer: C.24 km/hr
Explanation: Let distance between his home and hospital =
d
d km
Total distance travelled
=
d
+
d
=
2
d
=d+d=2d km
Total time taken
=
d
60
+
(
d
2
)
10
+
(
d
2
)
30
=d60+(d2)10+(d2)30
=
d
60
+
d
20
+
d
60
=
5
d
60
=
d
12
=d60+d20+d60=5d60=d12 hr
Average speed in the whole journey
=
2
d
(
d
12
)
=
2
d
×
12
d
=
24
=2d(d12)=2d×12d=24 km/hr
C
Question: How many total number of ways in which x distinct objects can be put into two different boxes is
A.n2
B.2x
C.2n
D.3n
Answer: B.2x
Explanation: Let the two boxes be B1 and B2. There are two choices for each of the x objects. So, the total number of ways is
2 × 2 ×.....× 2 (x times ) = 2x
Answer B
Question: Two dice are rolled. The probability of getting a sum of at least 9 is
A.13/36
B.5/18
C.35/36
D.11/36
Answer: B.5/18
Explanation: Sum of 9 = {(3,6) (6,3)} = 2ways.
Sum of 10 = {(5,5) (6,4) (4,6) (5,5)} = 4 ways.
Sum of 11 = {(6,5) (5,6)} = 2 ways.
Sum of 12 = {(6,6) (6,6)} = 2 ways.
Therefore, Favourable cases = 10
Total cases = 6 x 6 = 36.
Therefore, Probability = 10/36 = 5/18.
ANSWER:B
Question: An unbiased die is tossed. Find the probability of getting a multiple of 3.
A.1/2
B.1/6
C.2/3
D.1/3
Answer: D.1/3
Explanation: here s= {1,2,3,4,5,6}
let E be the getting of a multiple of 3.
then E = {3,6}
probability = 2/6 = 1/3
correct option is D
Question: when i was of 2 years old, my sister's age was half of mine..
now i am of 100..
what is the age of my sister??
A.98
B.99
C.97
D.95
Answer: B.99
Explanation: 99,one less than me.
ANSWER:B
Question: At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 5:5. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?
A.1/4
B.1/8
C.1/6
D.1/2
Answer: D.1/2
Explanation: Red: Blue = 5:5
Let Red = 5x and Blue = 5x
1/3 of Red are left handed => 1/3 * 5x = 5x/3 Red left handed
2/3 of Blue are left handed => 2/3 *5x = 10x/3 blue left handed
fraction of participants who are left handed = total left handed/ total participants = (red left handed + blue left handed)/total participants = (5x/3 + 10x/3)/(5x+5x) = (15x/30x) = 1/2
Answer : D
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
A.Rs.28,029
B.Rs.28,020
C.Rs.28,298
D.Rs.28,000
Answer: D.Rs.28,000
Explanation: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer: D
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is
A.1200
B.1764
C.1600
D.1354
Answer: B.1764
Explanation: Explanation:
Let P.W. be Rs.x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 189.
x × 16 × (9/12) × (1/100) = 189 or x = 1575.
P.W. = Rs. 1575.
Sum due = P.W. + T.D. = Rs.(1575
189) = Rs. 1764.
Answer: B
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?
A.299
B.112
C.500
D.167
Answer: C.500
Explanation: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer:C
Question: A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A.21
B.6
C.7
D.8
Answer: A.21
Explanation: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [385 * 3/55] sec
= 21 sec
Answer: A
Question: Tough and Tricky questions: Percents.
Over the course of a year, a certain microbrewery increased its beer output by 50 percent. At the same time, it decreased its total working hours by 0 percent. By what percent did this factory increase its output per hour?
A.125
B.130
C.150
D.155
Answer: C.150
Explanation: Lets assume the initial production was 100 litres of beer for 100 hr.
With the 50% increase the total amount of beer production will be 150 litres
100hr ----> 100 lts
1hr -----> 1 lts
100hr -----> 150 lts
1hr -----> 1.5 lts
Total Increase in production for 1 hr = 150%
Answer C
Question: Insert the missing number.
3, 9, 6, 6, 9, 3, 12, 0, 15, (....)
A.3
B.7
C.-3
D.8
Answer: C.-3
Explanation: Explanation:
There are two series, beginning respectively with 3 and 9. In one 3 is added and in another 3 is subtracted.
The next number is 0 - 3 = -3.
Answer: C) -3
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 50 per cent. The two reductions together are equal to a single reduction of
A.45%
B.62.5%
C.35%
D.32.5%
Answer: B.62.5%
Explanation: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 50percent is reduced which means the new price is merely 50percent of 3/4P
==> (3/4)x(1/2)P = 3/8P is the new price after both deduction which is 37.5percent of the original value P. This implies this entire series of deduction is worth having discounted 62.5% of P. So answer is B = 62.5%
Question: A certain city with a population of 180,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
A.a) 10,700
B.b) 15,000
C.c) 10,900
D.d) 11,000
Answer: B.b) 15,000
Explanation: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 180k
x = 15,000
Answer : B
Question: A ship sails 4 degrees north, then 13 S. then 17 N. then 24 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?
A.5
B.1
C.2
D.3
Answer: A.5
Explanation: Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 13 + 17 - 24 = -11
And x = 5.
Answer A
Question: In 1990 a total of u earthquakes occurred worldwide, some but not all of which occurred in Asia. If v o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
A.u/v
B.v/u
C.v/(u-v)
D.u/(u-v)
Answer: C.v/(u-v)
Explanation: We're given a couple of facts to work with:
1) There were a total of u earthquakes
2) Of those earthquakes, v of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Let's TEST VALUES
u = 5 total earthquakes
v = 2 occurred in Asia
Thus, there were 3 earthquakes that DID NOT occur in Asia....
The answer to the question is 2:3
We just need to plug in the values for u and v and find the match...
Answer A: u/v = 5/2 NOT a match
Answer B: v/u = 2/5 NOT a match
Answer C: v/(u-v) = 2/(5-2) = 2/3 This IS a match
Answer D: u/(u-v) = 5/(5-2) = 5/3 NOT a match
Answer E: 1 - (v/u) = 1-2/5 = 3/5 NOT a match
C
Question: Hannah and Jake race around a running track. Hannah runs at a constant rate of one lap every 2 minutes and Jake runs at a constant rate of one lap every 5 minutes. If they both start at the same time, how many minutes will it take for Hannah to get exactly one lap ahead of Jake?
A.3/5
B.5/3
C.7/3
D.10/3
Answer: D.10/3
Explanation: Let x be the number of minutes it takes for Hannah to get one lap ahead.
Then Hannah ran x/2 laps and Jake ran x/5 laps.
x/2 = 1+x/5
5x=10+2x
3x=10
x=10/3
The answer is D.
Question: A car covers a distance of 829 km in 7 hours. Find its speed?
A.104 kmph
B.289 kmph
C.118 kmph
D.277 kmph
Answer: C.118 kmph
Explanation: 829/7
= 118 kmph
Answer: C
Question: A 24 month project had a total budget of $44,400. After seventeen months, the project had spent $29,375. At this point, how much was the project under budget?
A.$1850
B.$1925
C.$2000
D.$2075
Answer: D.$2075
Explanation: Each month, the project should spend $44,400 / 24 = $1850.
In 17 months, the project should spend 17*$1850=$31,450.
The project is under budget by $31,450 - $29,375 = $2075.
The answer is D.
Question: The average of 13 numbers is 17.8. If the average of the first seven numbers is 17.6 and that of the last seven numbers is 17.4,then the middle number is?
A.11.8
B.11.9
C.12.2
D.13.6
Answer: D.13.6
Explanation: Middle number = 17.6*7 + 17.4*7- 17.8*13 = 123.2+121.8-231.4=13.6
Answer is D
Question: If $500 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years?
A.500 (1.056)(3)
B.500 (3+1.056)
C.500 (1+3(0.056))
D.500 (1.056)^3
Answer: D.500 (1.056)^3
Explanation: the formula is CI=P(1+r/100)^t
in this case i think D is the ans
Question: 20% of incoming freshman at a certain university have taken a calculus course. Among the incoming freshman who have not taken a calculus course, 148 have taken a pre-calculus course and 44 havent taken a precalculus couse. how many incoming freshman are there in the university?
A.60
B.120
C.180
D.240
Answer: D.240
Explanation: Soln:-
let the total incoming freshman be x.
given 20x/100 have taken calculus 1.
80x/100 have not taken calculus 1.
also given 80x/100 = 148+44
=> x = 240
ANSWER:D
Question: 6 friends go out to dinner at Outback Steakhouse. The total of their meal comes to 118.60 without a tip. They decide to leave a 20% tip to the waitress. They want to split the costs if the bill including the tip evenly among them. How much does each person have to pay if the bill is split evenly?
A.19.77
B.71.16
C.18.6
D.23.72
Answer: D.23.72
Explanation: The amount of the tip= 118.60*.20=23.72
118.60+23.62= 142.32 = amount of bill after the tip
142.32/6=23.72= amount each person must pay
The answer is D.
Question: How many words can be formed by using all letters of the word “BIHAR”
A.240
B.175
C.120
D.132
Answer: C.120
Explanation: The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
Ans: C
Question: A number x is multiplied by 5, 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 if x≠0 ?
A.25/9
B.9/5
C.5/3
D.3/5
Answer: C.5/3
Explanation: sqrt(5x/3) to be perfect square x has to 5/3
Ans: C
Question: The average earning of a mechanic for the first 4days of a week is Rs.18 and for the last four days is Rs.22. If he earns Rs.20 on the fourth day, his average earning forthe whole week is?
A.Rs. 10
B.Rs. 20
C.Rs. 30
D.Rs. 40
Answer: B.Rs. 20
Explanation: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -20
= Rs. 140
∴ Average earning = 140 / 7
= Rs. 20
B
Question: Jar A has 26% more marbles than Jar B . What percent of marbles from Jar A need to be moved into Jar B so that both jars have equal marbles?
A.7.6%
B.8.3%
C.9.6%
D.10.3%
Answer: D.10.3%
Explanation: An easy way to solve this question is by number plugging. Assume there are 100 marbles in Jar B then in Jar A there will be 126 marbles. Now, for both jars to have equal marbles we should move 13 marbles from A to B, which is 13/126=~10.3% of A.
Answer: D.
Question: Mary’s father is four times as old as Mary. Five years ago he was seven times as old. How old is mary?
A.6
B.8
C.10
D.12
Answer: C.10
Explanation: The problem involves age.
The question asks, “How old is each now?”, which means it’s asking for the ages of both
Mary and her father.
Let x Mary’s current age
4x Mary’s father’s current age
x-5 Mary’s age 5 years ago
4x-5 Mary’s father’s age 5 years ago
The problem states that 5 years ago, Mary’s father’s age 4x-5 was equal to seven
times Mary’s age7(x-5)
Write the equation.
4x-5=7(x-5)
4x-5=7x-35
30=3x
x=10
4x=40
Mary’s current age is 10 years old
correct answer C
Question: 9log9(5) = ?
A.1
B.2
C.3
D.5
Answer: D.5
Explanation: Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
9log9(5) = 5
correct answer D
Question: The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.10 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
A.a) $ 1.65
B.b) $ 2.00
C.c) $ 2.40
D.d) $ 2.70
Answer: A.a) $ 1.65
Explanation: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $1.1*1.5 = $1.65.
Answer: A.
Question: There are 10 oranges on a table, and a pair of oranges is to be selected. At most, how many different pairs are possible?
A.100
B.90
C.50
D.45
Answer: D.45
Explanation: N=10C2=10!/(8!2!)=10*9/2=45
Correct Answer: D
Question: Tary spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start?
A.$30
B.$35
C.$70
D.$105
Answer: C.$70
Explanation: Tary spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..
solution..
let the money be x..
2/5 is used...
1/2 of remaining 3/5 is put in savings account and remaining half is 21..
so 1/2 * 3/5 *x=21..
x=21*2*5/3=70..
C
Question: John deposited $10,000 to open a new savings account that earned 12 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?
A.$10,101
B.$10,609
C.$10,209
D.$10,601
Answer: B.$10,609
Explanation: 12 percent annual interest compounded quarterly --> 3% in 3 moths.
For the first 3 moths interest was 3% of $10,000, so $300;
For the next 3 moths interest was 3% of $10,000,plus9 earned on previous interest of $100, so $300+$9=$309;
Total interest for 6 months was $300+$309=$609, hence balance after 6 months was $10,000+ $609=$10,609.
Answer: B.
Question: 10 men,working 6 hours a day can complete a work in 18 days.How many hours a day must 15 men work to complete the same work in 12 days ?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: Solution
Let the required number of hours per day be x.
More men,Less hours per day (Indirect Proportion)
Less days,More hours per day (Indirect Proportion)
∴ 15 × 12 × x = 10 × 18 × 6 ⇔ x = 10x18x6/15x12 = x= 6. Answer A
Question: How many positive 5-digit integers have the odd sum B of their digits?
A.9*10^2
B.9*10^3
C.10^4
D.45*10^3
Answer: D.45*10^3
Explanation: We are looking at numbers between 10000 and 99999 both inclusive.
There are 90000 numbers.
Now for
10000 : sum of digits is odd;
10001 :sum of digits is even;
10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.
(Exception for the above statement :
When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd
and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)
This means exactly half of the numbers will have odd sum of their digits. i.e 45000
Answer :D
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
A.228
B.108
C.1266
D.188
Answer: B.108
Explanation: S = 180/6 * 18/5 = 108 kmph
Answer: B
Question: What is the product of all the possible values of x if x^2 - 2x - 8?
A.–29
B.–12
C.-8
D.29
Answer: C.-8
Explanation: Explanation:
=> y= x^2 - 2x - 8
=> y= (x+2) (x-4)
=> x= -2, y= 4
Product x = (-2)(4) = -8
answer option -8
ANSWER:C
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 12 hours, how many machines of type R were used?
A.1
B.4
C.6
D.9
Answer: A.1
Explanation: Rate of machine R =1/36
Rate of machine S =1/18
since same no of machines used for R and S to do the same work in 12 hrs
So collective rate needed to finish the work in 12 hrs= 1/12
Let the no of machine be x
So, x/36 +x/18 =1/12
x3/36=1/12
x=1
So no of machine R is 1
Answer A
Question: A dress on sale in a shop is marked at $X. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on thediscounted price. If a staff member buysthe dress what will she have to pay in terms of X?
A.0.555X
B.0.667X
C.0.765X
D.0.905X
Answer: C.0.765X
Explanation: If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85X = 0.765X
C