mathewhe/aqua_rat huggingface dataset:
Question: if integer N has p factors ; how many factors will 6N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: Case 1:
Let N = 6 => 2 x 3 (prime factorization) => p = 4;
6N = 36 => no. of factors = 9; (p+5)
Case 2:
Let N = 7 => p = 2;
6N = 42 => no of factors =8; (4p)
For different N different results are observed. So, shouldn't E be the right answer?
Answer: (E) Cannot be determined
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
(A) 2
(B) 22
(C) 23
(D) 26
(E) 30
Rationale: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on
2.
24-2=22
Option B
Answer: (B) 22
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 42 minutes. The waste pipe can empty the full cistern in?
(A) A)7
(B) B)6
(C) C)8
(D) D)9
(E) E)5
Rationale: 1/10 + 1/15 - 1/x = 1/42
x = 7
Answer:A
Answer: (A) A)7
Question: A person saved $10 in buying an item on sale. If he spent $400 for the item, approximately how much percent he saved in the transaction?
(A) 8%
(B) 10%
(C) 2%
(D) 2.4%
(E) 6%
Rationale: Actual price = 400+10 = $410
Saving = 10/410 * 100 = 100/41 = 2.4% approximately
Answer is D
Answer: (D) 2.4%
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
(A) 5litres, 7 litres
(B) 7litres, 4 litres
(C) 6litres, 6 litres
(D) 4litres, 8 litres
(E) 8litres, 10 litres
Rationale: Explanation:
Solution 1
Let x and (12âˆ’x) litres of milk be mixed from the first and second container respectively.
Amount of milk in x litres of the the first container =.75x
Amount of water in x litres of the the first container =.25x
Amount of milk in (12âˆ’xlitres of the the second container =5(12âˆ’x)
Amount of water in (12âˆ’x)litres of the the second container =.5(12âˆ’x)
Ratio of water to milk
Since x=6,12âˆ’x=12âˆ’6=6
Hence 6 and 6 litres of milk should mixed from the first and second container respectively.
Answer IS C
Answer: (C) 6litres, 6 litres
Question: Vijay bought 160 shirts at the rate of Rs. 220 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) s.225
(B) s.288
(C) s.485
(D) s.279
(E) s.282
Rationale: Total CP per shirt = 220 + 1400/160 + 1.75 + 320/160 = Rs. 232.5
SP = CP[(100 + profit%)/100]
= 232.5 * [(100 + 20)/100] = Rs.279.
Answer:D
Answer: (D) s.279
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 35 years, then find the age of the person sitting in the middle of the row?
(A) 9 years
(B) 29 years
(C) 18 years
(D) 19 years
(E) 16 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (35 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 35 * 3 = 196 - 75 - 105 = 16 years.
ANSWER:E
Answer: (E) 16 years
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 5 buckles is how many times that of 5 buckles and 6 buttons?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/5
(E) 5/6
Rationale: Let x be the weight of a button and let y be the weight of a buckle.
2x + 2y = (1/3)(3x+11y)
3x = 5y
x = 5y/3
3x + 5y = a(6x+5y)
10y = a(15y)
a = 10/15 =2/3
The answer is B.
Answer: (B) 2/3
Question: There are 10 pair of socks in a cupboard from which 4 individual socks are picked at random. The probability that there is at least one pair is:
(A) 195/323
(B) 99/323
(C) 198/323
(D) 185/323
(E) 115/323
Rationale: probability is 1-p(drawing four socks which ar different)
p(drawing four socks different) (20/20)*(18/19)*(16/18)*(14/17)=>224/323
so probability is 1-224/323=>99/323
ANSWER:B
Answer: (B) 99/323
Question: A teacher gave the same test to three history classes: W, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
(A) 74
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: Ans : B (75)
lets say class W indeed has 4 children, B has 6 children and C has 5 children.
now, if the average of class W is 65, hence total marks awarded in the class = 65*4=260
Similarly,
class B = 80*6 = 480
class C = 77*5 = 385
total marks provided = W+B+C = 260+480+385 = 1125
avg. marks = 1125 / 15 (total no. of students) = 75=B
Answer: (B) 75
Question: If n=(81!  − 80!  + 79!)/(79!), which of the following could be subtracted from n so that √n is an integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: first lets find n.
n=(81! −80! +79!)/(79!)
n=81! /79!−80!/79! +79!/79!
n=81∗80−80+1=80(81−1)+1=80^2+1
so what should be subtracted from80^2+1, so that it becomes a perfect square ..
ans is 1, as 80^2−1+1=80^2
ANSWER:A
Answer: (A) 1
Question: A man has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 70
(C) 50
(D) 80
(E) 60
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 320
16x = 320
x = 20.
Hence, total number of notes = 3x = 60.
Answer is E.
Answer: (E) 60
Question: 50 + 5 * 12 / (180/3) = ?
(A) 23
(B) 78
(C) 27
(D) 51
(E) 81
Rationale: Explanation:
50 + 5 * 12 / (180/3) = 50 + 5 * 12 / (60)
= 50 + (5 * 12)/60 = 50 + 1 = 51.
Answer:D
Answer: (D) 51
Question: The speed of light is approximately 1,76 * 10^5 miles per second. This approximate speed is how many miles per hour?
(A)  1,11 * 10^7
(B)  6,70 * 10^8
(C)  1,11 * 10^8
(D)  1,86 * 10^8
(E)  6,70 * 10^7
Rationale: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.
(1.76*10^5)*3600 = (1.76*10^5)*(3.6*10^3) = some number*10^8...
The key is realizing that thesome numberhas to be bigger thatn 1.76 (because 1.76*3.6), and the only answer that fits that is B
Answer: (B)  6,70 * 10^8
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 110 marks, the no of questions he attempts correctly is :
(A) 34
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 110
=> 5x = 170
=> x = 34
Answer: A
Answer: (A) 34
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be:
(A) 20 cm
(B) 25 cm
(C) 35 cm
(D) 50 cm
(E) None of these
Rationale: Explanation:
Total volume of water displaced =(4 x 50) m3 = 200 m3
Rise in water level = 200/40×20= 0.25m = 25cm
Answer: B
Answer: (B) 25 cm
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 4:7
(B) 4:9
(C) 4:3
(D) 4:6
(E) 4:2
Rationale: 12:9
= 4:3
Answer:C
Answer: (C) 4:3
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Sunday, what was the expected day when both the brothers were to return home and when did Rohit Return?
(A) Thursday, Monday
(B) Sunday, Thursday
(C) Wednesday, Sunday
(D) Monday, Friday
(E) none
Rationale: Rajat returned on Sunday -i.e. 3 days earlier
so actual day to return home is Wednesday.
Rohit returned after days so Sunday
ANSWER:C
Answer: (C) Wednesday, Sunday
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 187
(B) 180
(C) 289
(D) 216
(E) 279
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: (B) 180
Question: Two pipes A,B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.?
(A) 8 min
(B) 9 min
(C) 7 min
(D) 6 min
(E) 5 min
Rationale: work done by A => 18/24
work done by B => x/32
18/24 + x/32 = 1
3/4 + x/32=1
24+x=32 => x=8
ANSWER:A
Answer: (A) 8 min
Question: Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)?
(A) 2
(B) 4
(C) 7
(D) 9
(E) 10
Rationale: (21)(3^7) is divisible by 3 but 7 is not divisible by 3.
Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9.
The answer is D.
Answer: (D) 9
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 40% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
(A) $100
(B) b $115
(C) c $125
(D) d $50
(E) e $135
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 40% less than the price each head sold for on the day before i.e , (60/100)*0.5 = $ 0.3
Hence selling cost for the remaining cabbage = 500 * 0.3 = $ 150
Total selling cost = 500 + 150 = $ 650
Gross profit = $ 650 - $ 600 = $ 50
Hence Answer is D.
Answer: (D) d $50
Question: A machine puts c caps on bottles in m minutes. How many T hours will it take to put caps on b bottles?
(A) 60bm/c
(B) T=bm/60c
(C) bc/60m
(D) 60b/cm
(E) b/60cm
Rationale: The machine puts c caps in m minutes or c caps in m/60 hours.
Rate = c/m/60 = 60c/m.
To put b caps the machine will take:-
Time = Work/Rate
T = b/60c/m = bm/60c
Answer is B.
Answer: (B) T=bm/60c
Question: Raja was born 4 years after his father's marriage. His mother is 4 years younger than his father but 20 years older than Raja who is 20 years old. At what age did the father get married ?
(A) 30 years
(B) 25 years
(C) 20 years
(D) 22 years
(E) 21 years
Rationale: Explanation:
Raja's present age = 20 years.
His mother's present age = (20 + 20) years = 40 years.
His father's present age = (40 + 4) years = 44 years.
His father's age at the time of Raja's birth = (44 - 20) years = 24 years.
Therefore Raja's father's age at the time of marriage = (24 - 4) years = 20 years.
Answer: C
Answer: (C) 20 years
Question: Two integers are in the ratio of 1 to 3. If 10 is added to the smaller number, the ratio becomes 1 to 1. Find the larger integer.
(A) 6
(B) 9
(C) 10
(D) 12
(E) 15
Rationale: One option is to set up the equations and solve:
If the ratio of two integers x and y is 1 to 3, then 3x=y, where x is the smaller integer.
If adding 10 to the smaller integer makes the ratio 1 to 1, then x+10=y.
Substituting y=3x into the second equation yields x+10=3x.
So, x=5 (smaller integer) and, y=3x=15 (larger integer) so E is the correct answer.
Another option is to TEST the answer choices.
A) the larger number is 6
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 2
If 10 is added to the smaller number, the ratio becomes 1 to 1
If we add 10 to the smaller number (2), we get 12.
So, the new ratio is 12 to 6 which is the same as 2 to 1.
No good. We want a resulting ratio of 1 to 1
ELIMINATE A
B) the larger number is 9
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 3
If 10 is added to the smaller number, the ratio becomes 1 to 1
If we add 10 to the smaller number (3), we get 13
So, the new ratio is 13 to 9.
No good. We want a resulting ratio of 1 to 1
ELIMINATE B
C) the larger number is 10
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 3.33 (which is not an integer)
Since both numbers are integers, the larger number cannot be 10.
ELIMINATE C
D) the larger number is 12
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 4
If 10 is added to the smaller number, the ratio becomes 1 to 1
If we add 10 to the smaller number (4), we get 14
So, the new ratio is 14 to 12 which is 7 to 6.
No good. We want a resulting ratio of 1 to 1
ELIMINATE D
E) the larger number is 15
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 5
If 10 is added to the smaller number, the ratio becomes 1 to 1
If we add 10 to the smaller number (5), we get 15
So, the new ratio is 15 to 15. This is the same as the ratio of 1 to 1
Therefore E is the only correct choice.
Answer: (E) 15
Question: 95% of the house of a city is 7600. The total house of the city is?
(A) 7500
(B) 8250
(C) 10000
(D) 7750
(E) 8000
Rationale: X * (95/100) = 7600
X = 80 * 100
X = 8000
Answer: E
Answer: (E) 8000
Question: When I was married 10 years ago, my wife was the sixth member in the family. Today, my father died,and a baby was born to me. The average age in my family today is what it was when I was married.How old was my father when he died?
(A) 50 years
(B) 60 years
(C) 70 years
(D) 80 years
(E) Indeterminate
Rationale: If x was average age 10 years ago, then total age 10 years ago = 10x.
Total age of 6 persons before death of father = 10x+60
Total age of 6 persons ( excluding father and adding son of zero age) after death of father = 60x as average of family is x again.
Hence age of father at time of death = x+60-x = 60 years
ANSWER:B
Answer: (B) 60 years
Question: A boat can travel with a speed of 25km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 120km downstream.
(A) 1 hr
(B) 2 hrs
(C) 3 hrs
(D) 4 hrs
(E) 5 hrs
Rationale: Speed downstream = (25 + 5) km/hr = 30 km/hr.
Time taken to travel 120 km downstream = 120/30 hrs = 4 hrs.
Answer : D
Answer: (D) 4 hrs
Question: The ratio of male to female in a class is 3:4. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
(A) a)160 degree
(B) b) 168 degree
(C) c)264 degree
(D) d)192 degree
(E) e)204 degree
Rationale: let the common ratio be x.. so M=3x and F=4x and Total=7x
1/3 of M= 3x/3 and 2/3 of F= 8x/3
Total preferring that carrer = x+8x/3=11x/3
Now 5x= 360, so x=360/5=72..
so x*8/3= 72*11/3=192
C
Answer: (C) c)264 degree
Question: A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 32 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
(A) 2:5
(B) 5:14
(C) 3:5
(D) 4:7
(E) 14:5
Rationale: The first drink has 6 oz, which are 2 oz rum and 4 oz coke. The second drink is 32 oz, which are 8 oz rum and 24 oz coke. The resulting mixture is then 38 oz (10 oz rum and 28 oz coke). Overall, this is 10 oz rum: 28 oz coke, which is a 5:14 ratio.
Answer is B
Answer: (B) 5:14
Question: If x, y, and z are positive integers and 3x = 7y = 5z, then the least possible value of x + y + z is
(A) 15
(B) 25
(C) 71
(D) 35
(E) 45
Rationale: given 3x=7y=5z
x+y+z in terms of x
= x+(3x/7)+(3x/5) = 71x/35
now checking with each of the answers and see which value gives a minimum integer value.
A x = 35/71*15 , not an integer
B,D,E can be ruled out similarly.
C is minimum value as x = 71*35/71 = 35
Answer is C
Answer: (C) 71
Question: HCF and LCM two numbers are 14 and 396 respectively. If one of the numbers is 36, then the other number is?
(A) 36
(B) 66
(C) 154
(D) 264
(E) 364
Rationale: 14 * 396 = 36 * x
x = 154
ANSWER:C
Answer: (C) 154
Question: 99,995^2 - 5^2 =
(A) 10^10 - 2
(B) (10^5 – 2)^2
(C) 10^4(10^5 – 2)
(D) 10^5(10^5 – 10)
(E) 10^5(10^5 – 2)
Rationale: (99,995)^2 - (5)^2 = (100,000 -5)^2 - (5)^2 = (100,000)^2 - 2*5*100,000 + 5^2-5^2=(10^5)^2 - 10*(10^5) = 10^10 - 10*(10^5)=10^5(10^5 - 10) Answer D
Answer: (D) 10^5(10^5 – 10)
Question: Of the families in City X in 1994, 40 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. what percent of the families in City X owned a personal computer in 1998?
(A) 50%
(B) 52%
(C) 56%
(D) 70%
(E) 74%
Rationale: Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40
Number of families owning computer in 1998 = 40 * 130/100 = 52
Number of families in 1998 = 104
The percentage = 52/104 * 100 = 50%.
ANSWER:A
Answer: (A) 50%
Question: If 2805 / 2.55 = 1100, then 280.5 / 25.5 is equal to ?
(A) 1.01
(B) 1.1
(C) 0.11
(D) 11
(E) None
Rationale: Answer
Given expression 280.5 / 25.5 = 2805 / 255
= 2805 / (2.55 x 100)
= 1100 / 100
=11
Correct Option: D
Answer: (D) 11
Question: In a series of consecutive odd numbers, 27 is the eighth smallest number and 25 is the ninth largest number. What is the range of the series?
(A)  32
(B)  30
(C)  28
(D)  16
(E)  14
Rationale: Imp:All are consecutive odd numbers.
27 is the 8th smallest ,there are 7 numbers smaller then 27 ,smallest number :27-14=13
25 is the 10th largest ,so there are 8 numbers larger then 25, largest number:25+16=41
Range:41-13=28
Ans : C
Answer: (C)  28
Question: If q and t are positive integers, qt + q + t cannot be
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let qt + t +q = x
Add 1 on both sides:
qt + t + q + 1 = x + 1
tq + 1) + q + 1 = x + 1
(q + 1)(t + 1) = x + 1
Minimum value of (q + 1) = 2
Minimum value of (t + 1) = 2
Hence x + 1 cannot be prime
Substitute x from the given options: 6 + 1 = 7 --> prime --> qt + t + s cannot be 6
Answer: B
Answer: (B) 6
Question: A basketball player is shooting hoops. He shoots a free throw, a high school 3-pointer, and then a professional 3-pointer. The probability that he makes the free throw is 4/5, the probability that he makes the high school 3-pointer is 1/2, and the probability that he makes the professional 3-pointer is 1/3. What is the probability that he makes at least one of the three shots?
(A) 14/15
(B) 15/16
(C) 17/18
(D) 9/10
(E) 5/6
Rationale: The probability that he makes at least one of the three shots = 1 - (the probability that he misses all of the shots)
The probability that he misses all shots = (prob that he misses free throw)*(prob that he misses 3-pointer)*(prob that he misses the professional 3-pointer)
Prob that he misses the free throw = 1 - 4/5 = 1/5; Prob that he misses the 3-pointer = 1 - 1/2 = 1/2; Prob that he misses the professional 3-pointer = 1 - 1/3 = 2/3
Thus the probability that he misses all shots = (1/5)*(1/2)*(2/3) = 1/15
Answer: 1 - 1/15 = 14/15
A
Answer: (A) 14/15
Question: A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is
(A) 16
(B) 14
(C) 15
(D) 18
(E) 20
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 20) years
=> (x + 20) + 2 = 2(x + 2)
=> x + 22 = 2x + 4
So, x = 18. Answer: D
Answer: (D) 18
Question: The compound ratio of 2/3, 6/7, 1/3 and 3/8 is given by?
(A) 7/98
(B) 1/48
(C) 1/98
(D) 1/96
(E) 3/42
Rationale: 2/3 * 6/7 * 1/3 * 3/8 = 36/504 = 3/42
ANSWER:E
Answer: (E) 3/42
Question: The average age of 6 men increases by 3 years when two women are included in place of two men of ages 24 and 26 years. Find the average age of the women?
(A) 37
(B) 26
(C) 34
(D) 18
(E) 11
Rationale: Explanation:
24 + 26 + 6 * 3 = 68/2 = 34
Answer: C
Answer: (C) 34
Question: A factory produces 8000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
(A) 4436 toys
(B) 5487 toys
(C) 2000 toys
(D) 2354 toys
(E) 1375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
8000 /4 = 2000 toys
correct answer C
Answer: (C) 2000 toys
Question: There are 760 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
(A) 320
(B) 345
(C) 425
(D) 475
(E) 400
Rationale: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 760. Hence
3x + 5x = 760
Solve for x
8x = 760
x = 95
Number of boys
3x = 3 × 95 = 285
Number of girls
5x = 5 × 95 = 475
D
Answer: (D) 475
Question: a boatman selling a boat along river flow.if he sell boat in steal water at 3m/sec and flow of river is 2m/sec.how much time he will take to sell 100m.
(A) 30
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: net speed = 3+2=5 m/sec
distance = 100m
time=100/5=20sec
answer D
Answer: (D) 20
Question: If a and b are multiples of 9 then which are all the multiples of 9
1) a*b
2) a/b
3) a+b
4) a-b
5) a^b
(A) 1,2,5
(B) all of these
(C) 1,3,4,5
(D) 2,3,4,5
(E) 1,3
Rationale: a*b a^b a+b a-b are multiples of 6 except a/b
ANSWER:C
Answer: (C) 1,3,4,5
Question: Mark has a rectangular driveway with a line painted diagonally across. The length of the driveway is 6 feet longer than its width. If the total area of the driveway is 40 square feet, what is the length of the painted line (in feet)?
(A) Between 9 and 10
(B) Between 10 and 11
(C) Between 11 and 12
(D) Between 12 and 13
(E) Between 13 and 14
Rationale: To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have
x(x + 6) = 40. By putting the equation in standard form, we get x^2+6x-40=0. By using the quadratic formula, we get roots of 4 and -10. We know that x is the width, and x+6 is the length, so by using the roots, we get 4 as the width (x), and 10 as the length (x+5).
Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=4^2+10^2
=16+100
=116
The square root of 97 is more than 10, since 10^2 = 100. Going up a number, we can compute 11^2 = 121 >116. Therefore, the length of the diagonal must be between 10 and 11.
The correct answer is B.
Answer: (B) Between 10 and 11
Question: Which greatest possible length can be used to measure exactly 15 meter 20 cm, 12 meter 20 cm and 14 meter 20 cm
(A) 20cm
(B) 25cm
(C) 24cm
(D) 55cm
(E) 30cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1520 cm, 1220cm, 1420cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 20.
Option A
Answer: (A) 20cm
Question: The sum of five numbers is 100. The average of the first two numbers is 10 and the third number is 30. Find the average of the two numbers?
(A) 25
(B) 20
(C) 23
(D) 22
(E) 30
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 100
(P + Q)/2 = 10 and R = 30
P + Q = 20 and R = 30
P + Q + R = 50
S + T = 100 - (P + Q + R) = 50
Average of the last two numbers
= (S + T)/2 = 25
Answer:A
Answer: (A) 25