divelab/Sys2Bench huggingface dataset:
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
Options:
A)156
B)150
C)137
D)132
E)89
Rationale: Let x be the original 2-digit number.
If each digit is halved, then the sum of G and H is 3x/2.
Note the sum must be a multiple of 3 and less than 150.
Only 132 satisfies these two conditions.
The answer is D.
Answer: D
Question: The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
A)29997
B)28088
C)27098
D)19000
E)2799
Rationale: Money paid in cash = Rs. 1000
Balance payment = (20000 - 1000) = Rs. 19000.Answer:D
Answer: D
Question: A merchant marks his goods up by 50% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
Options:
A)21%
B)25%
C)69%
D)35%
E)19%
Rationale: Let the price be 100.
The price becomes 150 after a 50% markup.
Now a discount of 10% on 150.
Profit=135-100
35%
answer D
Answer: D
Question: In a certain school, the ratio of boys to girls is 5 to 13. If there are 160 more girls than boys, how many boys are there?
Options:
A)100
B)36
C)45
D)72
E)117
Rationale: The ratio of b to G is 5:13 and the other data point is G are more than boys by 160...
Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 160. so 1 part corresponds to 160/8=20 and so
5 parts correspond to 5*10 = 100.
A
Answer: A
Question: If p and q are both odd prime numbers andp < q, then how many different positive integer factors does2pqhave?
Options:
A) 3
B) 4
C) 6
D) 8
E) 12
Rationale: p and q are both odd prime numbers- It means either p or q is not 2
and since prime numbers have only two factors - 1 and the number itself
p and q each will have (1+1)= 2 factors
Hence 2pq will have (1+1)(1+1)(1+1)= 8 factors
D is the answer
Answer: D
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31
Options:
A)2
B)3
C)5
D)7
E)8
Rationale: P ÷ 44 = 432
=> P = 432 * 44 = 19008
P / 31 = 19008 / 31 = 613, remainder = 5
C
Answer: C
Question: If the cost price of 35 chocolates is equal to the selling price of 21 chocolates, the gain percent is :
Options:
A)66.55%
B)66.66 %
C)66 %
D)55%
E)66.33%
Rationale: Explanation :
Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 21 chocolates = Rs. 21;
S.P. of 21 chocolates =Rs. 35.
.'. Gain% = 14*100/21 = 66.66%
Answer : B
Answer: B
Question: A coin is tossed 6 times. What is the probability that the number of Heads is equal to the number of Tails?
Options:
A)5/16
B)4/13
C)7/16
D)5/12
E)6/17
Rationale: We have to find the probability that we get 3 heads and 3 tails in 6 tosses of the coin.
Using the binary formula and defining a head as a success,
P(3 heads in 6 tosses) = 6C3* (1/2)^2 * (1/2)^2*(1/2)^2
= 20/64
= 5/16
The answer is A
Answer: A
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
Options:
A)1/122
B)1/129
C)1/121
D)1/128
E)1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= 4C4/9C4
= 1/126
Answer: E
Answer: E
Question: (1000)7÷(10)19=?
Options:
A)10
B)100
C)1000
D)10000
E)None of these
Rationale: Explanation:
=(103)7/(10)19
=(10)21/(10)19=10(2)=100
Option B
Answer: B
Question: In a class of 30 students in an examination in maths 3 students scored 95 marks each, 3 get zero each and the average of the rest was 45. What is the average of the whole class?
Options:
A)A)47
B)B)45.6
C)C)44
D)D)48.5
E)E)49
Rationale: Explanation:
Total marks obtained by a class of 25 students
= 3*95 + 3*0 + 26 * 45 =1455
Average marks of whole class = 1455/30 =48.5
Answer: Option D
Answer: D
Question: A certain auto manufacturer sold 4% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
Options:
A)63,000
B)2,000,000
C)2,020,000
D)2,040,000
E)2,300,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-4/100(X)
If sales in 2006,X= 2.1 million find X-4/100(X)
(2.1 x 10^6)-4/100(2.1 x 10^6)
2100000-84000=2,016,000-----> 2,020,000(approx)
ANSWER:C
Answer: C
Question: Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 11 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 11 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 11-3 = 8. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer A
Answer: A
Question: In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,9). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
Options:
A)1/5
B)1/3
C)1/2
D)2/9
E)4/5
Rationale: The area of the right triangle is (1/2)*4*9 = 18.
Only the points (a,b) below the line y=x satisfy a - b > 0.
The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.
P(a - b > 0) = 8/18 = 2/9
The answer is D.
Answer: D
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)10
B)12
C)16
D)18
E)20
Rationale: Explanation:
10 * 15 + 36 – 26 = 160/10 = 16
C)
Answer: C
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many ways can they selected that at least one boy should be there?
Options:
A)159
B)194
C)205
D)209
E)140
Rationale: We may have( 1 black and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4boys)
=(6c1 x 4c3)+(6c2 x 4c2)+(6c3 x 4c1)+6c4
=24+90+80+15
=209
ANSWER D 209
Answer: D
Question: If 3 people can do 3 times of a particular work in 3 days, then how many days would it take 5 people to do 5 times of that particular work?
Options:
A)1
B)2
C)3
D)5
E)8
Rationale: 3 people can do the work one time in one day.
1 person can do 1/3 of the work in one day.
5 people can do 5/3 of the work in one day.
5 people can do 5 times the work in 3 days.
The answer is C.
Answer: C
Question: A certain quantity of 80% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
Options:
A)1/4
B)1/3
C)1/2
D)2/3
E)9/11
Rationale: Let's say that the total original mixture A is 100 ml
The original mixture A thus has 50 ml of alcohol out of 100 ml of solution
You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 80 ml and 25 ml is 55 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 25%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 45%. Therefore, 45 out of 55 is 9/11 and E is the answer.
Answer: E
Question: In the faculty of Reverse-Engineering, 300 second year students study numeric methods, 600 second year students study automatic control of airborne vehicles and 200 second year students study them both. How many students are there in the faculty if the second year students are approximately 70% of the total?
Options:
A)750
B)800
C)900
D)950
E)1000
Rationale: Total number of students studying both are 300 + 600 - 200 = 700 (Subtracting the 200 since they were included in the both the other numbers already).
So 70% of total is 700, so 100% is 1000
Answer is E
Answer: E
Question: Length of a rectangular plot is 40 mtr more than its breadth. If the cost of fencin g the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)46 m
B)60 m
C)58 m
D)70 m
E)80 m
Rationale: Let breadth = x metres.
Then, length = (x + 40) metres.
Perimeter = 5300/26.5 m = 200 m.
2[(x + 40) + x] = 200
2x + 40 = 100
2x = 60
x = 30.
Hence, length = x + 40 = 70 m
D
Answer: D
Question: Which of the following is the lowest positive integer that is divisible by the first 6 positive integer multiples of 3?
Options:
A)90
B)100
C)120
D)150
E)180
Rationale: The number must be divisible by 3, 2*3, 3^2, 2^2*3, 5*3, and 2*3^2.
The lowest such number is 2^2*3^2*5 = 180.
The answer is E.
Answer: E
Question: Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?
Options:
A)3 : 1
B)7 : 3
C)3 : 2
D)4 : 5
E)3 : 4
Rationale: The lemonade is 50% water and 20% sugar.
The limeade is 40% water and 32% sugar.
The crusade is more than 45% water and more than 24% sugar.
For the crusade to be 45% water, the ratio of lemonade to limeade must 1:1. Since the crusade is more than 45% water (the average of 50 and 40), then the ratio of lemonade to limeade must be more than 1:1. Eliminate D and E.
For the crusade to be 24% sugar, the ratio of lemonade to limeade must 2:1. Since the crusade is more than 24% water, then the ratio of lemonade to limeade must be less than 2:1. Eliminate A and B.
Answer: C.
Answer: C
Question: 9.99 x 9.9 x 9 ÷ 9.9 ÷ 0.3 = ?
Options:
A)276
B)299
C)310
D)3.33
E)365
Rationale: Explanation:
? = (9.99 x 9.9 x 9)/(9.9 x 0.9 x 0.3) = 3.33
Answer: Option D
Answer: D
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Options:
A)28
B)27
C)29
D)24
E)20
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40
= 9/2 => x
= 20 km.
Answer: E
Answer: E
Question: The sum of digits of a two digit number is 13,The difference between the digits is 5. Find the number
Options:
A)85
B)94
C)83
D)72
E)None
Rationale: Description :
=> x+y=13, x-y=5
Adding these 2x =18
=> x=9, y=4.
Thus the number is 94
Answer B
Answer: B
Question: Which number is the odd one out?
159
248
840
357
591
582
Options:
A)120
B)240
C)840
D)360
E)160
Rationale: C
840
In the rest there is the same difference between each digit, eg: 8 (Ã¢â‚¬â€œ4) 4 (Ã¢â‚¬â€œ4)0
Answer: C
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
Options:
A)187
B)476
C)268
D)208
E)276
Rationale: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x
= 476
Answer: B
Answer: B
Question: Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was
Options:
A)2:1
B)3:2
C)4:3
D)5:4
E)1:2
Rationale: Explanation:
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 3 : 2. Answer: B
Answer: B
Question: At present, the ratio between the ages of Arun and Deepak is 4:8. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
Options:
A)17 years
B)15 years
C)18 years
D)40 years
E)19 years
Rationale: Let the present ages of Arun and Deepak be 4x and 8x years respectively.
Then, 4x + 6 = 26 => x
= 5
Deepak's age
= 8x
= 40 years.
Answer:D
Answer: D
Question: A new sales clerk in a department store has been assigned to mark sale items with red tags, and she has marked 30% of the store items for sale. However, 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. What percent of the items that are marked for sale are supposed to be marked with regular prices?
Options:
A)30%
B)35%
C)40%
D)45%
E)50%
Rationale: # of items 100 (assume);
# of items that should be marked for sale is x;
# of items that should be at the regular price is 100-x;
# of items that are actually marked for sale 0.3*100=30.
Let's see how many items are marked for sale:
20% of 100-x (20% of the items that are supposed to be marked with their regular prices (100-x) are now marked for sale);
100-55=45% of x (since 55% of the items that are supposed to be marked for sale (x) are marked with regular prices, then the remaining 45% of x are marked for sale);
So, 0.2(100-x)+0.45x=30 --> x=40 (# of items that should be marked for sale).
So, # of the items that are supposed to be marked with their regular prices is 0.2*(100-40)=12, which is 12/30*100=40% of # of items that are actually marked for sale.
Answer: C.
Answer: C
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 38,000, what will be the amount A receives?
Options:
A)14700
B)15960
C)14900
D)14300
E)14000
Rationale: Total amount invested = 50000
Assume that investment of C =x.
Then investment of B =5000+x,
Investment of A =4000+5000+x=9000+x
x+5000+x+9000+x=50000
⇒3x+14000=50000
⇒3x=50000–14000=36000
⇒x=36000/3=12000
Investment of C =x=12000
Investment of B =5000+x=17000
Investment of A =9000+x=21000
Ratio of the investment of A, B and C
=21000:17000:12000
=21:17:12
Share of A = Total profit ×21/50
=38000×21/50=15960
Answer is B
Answer: B
Question: Ms.James invested in Fund T and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund T paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund T. How much did Ms. Morris invest in Fund T?
Options:
A) $32,000
B) $36,000
C) $40,000
D) $42,000
E) $45,000
Rationale: 0.17B-0.23T = 200 | * 100
17B-23T=20,000
T+B=100,000
B=100,000 - T
17(100,000 - T) - 23T = 20,000
1,700,000 - 17T - 23T = 20,000
1,680,000 = 40T
divide by 40
first two digits: 42...so answer is D.
Answer: D
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 16%?
Options:
A)20%
B)26%
C)13 1/30%
D)12%
E)13%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 84
2/3 SP1 = 84
SP1 = 126
100 --- 26 => 26%
ANSWER:B
Answer: B
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)Rs.3250
B)Rs.6250
C)Rs.10250
D)Rs.11750
E)Rs.12750
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
ANSWER:D
Answer: D
Question: The average age of husband, wife and their child 3 years ago was 33 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Options:
A)35 years
B)40 years
C)50 years
D)58 years
E)None
Rationale: Solution
Sum of the present ages of husband, wife and child	= (33x3+3x3) years
= 108 years.
Sum of the present ages of wife and child	= (20x2+5x2) years
= 50 years.
âˆ´ Husband's present age	= (108 - 50) years
= 58 years.
Answer D
Answer: D
Question: A sum of Rs. 2900 amounts to Rs. 3422 in 3 years. Had the rate of interest be 2% higher then what would the sum amount in the same time period?
Options:
A)Rs. 4465
B)Rs. 3683
C)Rs. 3596
D)Data inadequate
E)None of these
Rationale: 3422=2900+(2900*R*3/100)
R=6
If R is 2 more.
Then R=8
Sum=2900+(2900*8*3/100)
Sum=3596
ANSWER:C
Answer: C
Question: J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to
Options:
A)22
B)14
C)6
D)8
E)16
Rationale: Given J > P
J + P = 7, only options are (6, 1), (5, 2), (4, 3)
From the given options, If J = 4 the P = 3. Times taken by them = 244+243=14
Answer:B
Answer: B
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 140 of the workers of that company are men, how many of the workers are women?
Options:
A)85
B)95
C)105
D)120
E)210
Rationale: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.
Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.
Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.
Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.
If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.
Cavg = (80*1 + 40*2)/3 = 160/3% are men
Total = 120*300/160 = 225
No. of women = 225 - 140 = 85
A
Answer: A
Question: An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is:
Options:
A)2/91
B)1/22
C)3/22
D)2/77
E)None of these
Rationale: Explanation :
Let S be the sample space.
Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455
Let E = event of getting all the 3 questions from simple mathematics section.
n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10
P(E) = n(E)/n(S) = 10/455 = 2/91 .
Answer : A
Answer: A
Question: In a group of 100 cars, 49 cars do not have air conditioning. If at least 51 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?
Options:
A)49
B)47
C)48
D)51
E)53
Rationale: Lets assume AC=51(includesonly AC carsandcars with AC and racing stripes)
lets assume RS(racing stripes)>=51(includescars with AC and racing stripesandonly racing stripes).
Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=51.. we have to assign atleast 2 tocars with AC and racing stripes.
Hence AC=51-2=49.
The answer is A
Answer: A
Question: A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?
Options:
A)69.5 km/hr
B)70 km/hr
C)79 km/hr
D)79.2 km/hr
E)79.5 km/hr
Rationale: Explanation:
Let the length of the train be x metres and its speed by y m/sec.
Then,
Now,
8y + 264 = 20y
y = 22.
Speed = 22 m/sec = km/hr = 79.2 km/hr.
ANSWER IS D
Answer: D
Question: 765 chairs are to be arranged in a column in such a way that the number of chairs in each column should be equal to the columns. How many chairs will be excluded to make this arrangement possible?
Options:
A)6
B)36
C)19
D)27
E)None of these
Rationale: 27(2) < 765 < 28(2)
∴ required no. of chairs to be excluded
= 765 – 729 = 36
Answer B
Answer: B
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 20 miles per gallon, and from Town B to Town C, the car averaged 25 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
Options:
A)20
B)18
C)21.4
D)16
E)10
Rationale: step 1) took LCM of 20 and 25.. came as 100.
step 2) 100 distance between B to C... do 100/25 hence 4 gallons used
step 3) twice distance.. hence 100*2= 200... do as above.. 200/20= 10 gallons used
step 4) total gallons.. 4+10= 14 gallons
step ) total miles= 100+200= 300 miles
hence.. average of whole journey = 300/14 which comes to 21.4
Answer : C
Answer: C
Question: A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 bours each. How long will they take to do it, working together 8 hours a day?
Options:
A)8 days
B)2 days
C)7 days
D)1 day
E)3 days
Rationale: A can complete the work in (7 x 9) = 63 hours.
B can complete the work in (6 x 7) = 42 hours.
A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)
(A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)
Both will finish the work in (126/5) hrs.
Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)=3 days
Answer is E.
Answer: E
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Options:
A)5/21
B)5/81
C)5/29
D)9/21
E)5/61
Rationale: Explanation:
Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252 = 5/21
Answer: Option A
Answer: A
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 144 km/hr
Options:
A)5 seconds
B)4.5 seconds
C)3 seconds
D)2.5 seconds
E)None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 144*(5/18) = 40 m/sec
Time = Distance/speed
= 100/40 = 2.5 seconds
Answer: D
Answer: D
Question: Find the odd man out. 3576, 1784, 888, 440, 216, 105, 48
Options:
A)1784
B)888
C)216
D)105
E)48
Rationale: 3576
(3576-8)/2 = 1784
(1784-8)/2 = 888
(888-8)/2 = 440
(440-8)/2 = 216
(216-8)/2 = 104
(104-8)/2 = 48
Hence, 105 is wrong. 104 should have come in place of 105
Answer is D
Answer: D
Question: In how many different ways can 3 identical gold shirts and 3 identical sliver shirts be distributed among 6 children such that each child receives a shirt?
Options:
A)100
B)400
C)20
D)96416
E)62
Rationale: Approach 1:
1st Child: 6 has options
2nd Child: 5 has options…
Therefore, for all kids: 6 x 5 x 4 x 3 x 2 = 720 arrangements.
Since the golds are identical, we divide by 3!; Since the silvers are identical, we divide by another 3!
So: in all, 720/[ 3! X 3! ] = 20 ways.
(e.g. Answer: C)
Answer: C
Question: If 5^z is a factor of 160!, which of the following could be the value of z?
Options:
A)40
B)32
C)51
D)39
E)60
Rationale: 5^z is a factor of 160!, what values can z take.
Powers of 5 in 160! = [160/5] + [160/25] +[160/125] , where [x] is the integral part of x
Powers of 5 in 160! = 32 + 6 + 1 = 39
Hence the maximum value of 5^z in 160! = 5^39
Correct Option: D
Answer: D
Question: In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = h is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-h, -k), then what are the coordinates of the point P?
Options:
A)(-5h, -5k)
B)(-3h, -3k)
C)(2h, 2k)
D)(3h, 3k)
E)(5h, 5k)
Rationale: firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-h, -k), so R is at a distance of 2h from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4h and coord (3h,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3h,3k).
ANSWER:D
Answer: D