mathewhe/aqua_rat huggingface dataset:
Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 12:00 a.m., at what time was it one-eighth full?
(A) 9:00 a.m.
(B) 7:00 a.m.
(C) 6:00 a.m.
(D) 4:00 a.m.
(E) 11:00 a.m.
Rationale: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 12:00 a.m -1 hour = 11:00 a.m.
Answer: E.
Answer: (E) 11:00 a.m.
Question: In given series 7 8 16 46 107 232 448 only one number is incorrect. Find out that wrong number.
(A) 8
(B) 16
(C) 46
(D) 107
(E) 232
Rationale: (N+1)th term = Nth term +(N)^3
8=7+1^3
16=8+2^3
43= 16+3^3............. so 46 is wrong.
107= 43+4^3
232= 107+5^3
448= 232+6^3
ANSWER:C
Answer: (C) 46
Question: If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is?
(A) 1:1
(B) 2:1
(C) 3:1
(D) 4:1
(E) 5:1
Rationale: B
2:1
Let 1 man's 1 day work = x and 1 boy's 1 day work = y.
Then, 12x + 16y = 1/5 and 13x + 24y = 1/4
Solving these two equations, we get:
x = 1/100 and y = 1/200
Required ratio = x:y = 1/100 : 1/200 = 2:1.
Answer: (B) 2:1
Question: A committee of 6 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee?
(A) 1/28
(B) 3/28
(C) 1/14
(D) 360/14
(E) 3/14
Rationale: 3/8*4/7*1/6*6! = 3/14. We are multiplying by 6! because we can choose secretary,economist, and accountant is several way:
Answer: D.
Answer: (D) 360/14
Question: If 6 - 12/X = 7 - 7/X, then X =
(A) -5
(B) 19
(C) -7/5
(D) 1
(E) 5/6
Rationale: We're given the equation 6 - 12/X = 7 - 7/X. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...
6X - 12X/X = 7X - 7X/X
We can then eliminate that denominator, which gives us....
6X - 12 = 7X - 7
-5 = X
A
Answer: (A) -5
Question: If y ¤ s = y^(2s) for all positive integers, then (3 ¤ 4) ¤ 2 =
(A) 3^8
(B) 3^12
(C) 3^16
(D) 3^24
(E) 3^32
Rationale: y ¤ s = y^(2s)
3 ¤ 4 = 3^(8)
(3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32
Correct Option: E
Answer: (E) 3^32
Question: Faiza has 7 purses, she gives 3 purse as gift. Now how many purse did she have ?
(A) 2
(B) 5
(C) 11
(D) 9
(E) 4
Rationale: 7-3=4. Answer is E
Answer: (E) 4
Question: If shares of two persons in profits are Rs.400 and Rs.800 then ratio of their capitals is
(A) 3:4
(B) 2:3
(C) 4:3
(D) 1:3
(E) 1:2
Rationale: profit=time*capital
so 400:800=1:2
ANSWER:E
Answer: (E) 1:2
Question: Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
(A) 16537.52
(B) 16537.29
(C) 16537.5
(D) 16537.2
(E) 16537.11
Rationale: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year
= 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20)
= Rs.16537.50
Answer:C
Answer: (C) 16537.5
Question: A shopkeeper forced to sell at cost price, uses a 750 grams weight for a kilogram. What is his gain percent?
(A) 10%
(B) 9%
(C) 33.33%
(D) 12 %
(E) None of these
Rationale: Shopkeeper sells 750g instead of 1000g.
So, his gain = 1000 - 750 = 250g.
Thus, %Gain = (250 *100)/750 = 33.33%.
answer : OPTION C
Answer: (C) 33.33%
Question: 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required?
(A) 5 days
(B) 6 days
(C) 7 days
(D) 8 days
(E) 10 days
Rationale: That is, 1 work done = 12 × 8 × 10
Then, 12 8 × 10 = ? × 15 × 8
? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days
D)
Answer: (D) 8 days
Question: A man has Rs. 480 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) 10
(C) 20
(D) 50
(E) 80
Rationale: Explanation:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer is A
Answer: (A) 90
Question: A passenger sitting near the window in a train moving at 30 km/h, noticed that it took 3 sec. for the oncoming train to pass by. What was the speed of the oncoming train if the length of the oncoming train was 75 metres?
(A) a)50km/h
(B) b)52km/h
(C) c)56km/h
(D) d)60km/h
(E) e)70km/h
Rationale: im getting A
3 secs to pass a 75 mts train , therefore speed = 25 meters/sec
to convert m/s to km/hrs multiply by 3.6
25*3.6 = 90
so its 90-30 = 60 .
D
Answer: (D) d)60km/h
Question: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 41
(B) 45
(C) 42
(D) 14
(E) 15
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42
Answer: C
Answer: (C) 42
Question: Solve the given two equations and find the inequality of X and Y. (a) 2x^2 + 11x + 14 = 0 and (b) 4y^2 + 12y +9 =0
(A) If x>y
(B) If x>=y
(C) If x < y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=-7/2 or -2
Y=-3/2
If x<y
C)
Answer: (C) If x < y
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 2%. What is the cost price?
(A) s.1000
(B) s.1009
(C) s.1166.7
(D) s.1006
(E) s.1002
Rationale: Explanation:
90%
102%
--------
12% ---- 140
100% ---- ? => Rs.1166.7
Answer:C
Answer: (C) s.1166.7
Question: If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend?
(A) A)$57.45
(B) B)$35.42
(C) C)$60.60
(D) D)$21.56
(E) E)$72.60
Rationale: The tip is 20% of what he paid for lunch.
tip = 20% of 60.50 = (20/100)*60.50 = $12.10
Total spent
60.50 + 12.10 = $72.60
correct answer is E)$72.60
Answer: (E) E)$72.60
Question: Which of the following best approximates the value of p if 5^30+3^11=5^p ?
(A) 39
(B) 30
(C) 28
(D) 27
(E) 17
Rationale: We have: 5^30+3^11=5^p
==> because 3^11 > 0 --> 5^p MUST be equal or greater than 5^30 ==>p MUST be equal or greater than 30
==> Options C, D, and E are out immediately.
Divide both sides by 5^p and p >= 30
We have:
5^(30-p) + 3^11/5^p = 1
Because p >= 30 ==>3^11/5^p = 0.0000xyz, that is very small,we can ignore it.
Thus, 5^(30-p) must be approximately 1
==> 30-p = 0 ==> p is approximately 30
B is the answer.
Answer: (B) 30
Question: IF
11= N
12= E
13= N
14= N
15= N
THEN 16=?
(A) I
(B) J
(C) K
(D) L
(E) N
Rationale: IF
11= N... last letter of eleven
12= E.... last letter of Twelve
13= N
14= N
THEN 16=N... last letter of Sixteen
ANSWER:E
Answer: (E) N
Question: After 38 liters of petrol were poured into the tank, it was still 5% empty. How much petrol must be poured into the tank in order to fill it?
(A) 7 liters
(B) 9 liters
(C) 5 liters
(D) 2 liters
(E) 2 liters
Rationale: Explanation:
95% ----------- 38
5% ------------ ? => 2 liters
Answer: D
Answer: (D) 2 liters
Question: A data set with a mean of 40 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?
(A) 18
(B) 36
(C) 59
(D) 63.5
(E) 65
Rationale: One standard deviation of the mean is from{mean}-{deviation}=40-3.5=36.5 to{mean}+{deviation}=40+3.5=43.5. The smallest number within this range from the options is 36.
Answer: B.
Hope this helps.
Answer: (B) 36
Question: A reduction of 42% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 2.15
(B) 8.15
(C) 7.15
(D) 3.15
(E) 1.15
Rationale: Explanation:
40*(42/100) = 16.8 --- 64
? --- 12 => Rs.3.15
Answer: D
Answer: (D) 3.15
Question: Departments A, B, and C have 5 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?
(A) 19,000
(B) 23,750
(C) 100,000
(D) 190,000
(E) 400,000
Rationale: 5c1 * 5c1* 5c1*20c2 = 5*5*5*190=23,750. Hence B is the correct answer.
Answer: (B) 23,750
Question: The average age 9 members of a committee are the same as it was 3 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 20 years
(B) 27 years
(C) 18 years
(D) 29 years
(E) 30 years
Rationale: 9 * 3 = 27 years
Answer:B
Answer: (B) 27 years
Question: If w,x,y,z are consecutive positive integers ; then which of the following is always even?
[1] w*x+(y+2)^2*z
[2] w^x + z^y
[3] 6z^2
(A) 1
(B) 2
(C) 3
(D) 1 and 2
(E) 1 and 3
Rationale: Plug in some numbers
w = 1
x = 2
y = 3
z = 4
Check the options -
[1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number }
[2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number }
[3] 6z^2 =6*4^2 even
[1] and [3]
E
Answer: (E) 1 and 3
Question: Rs. 5625 is to be divided among A, B and C so that A may receive 1/2 as much as B and C together receive and B receives 1/4 of what A and C together receive. The share of A is more than that of B by
(A) 237
(B) 279
(C) 271
(D) 750
(E) 112
Rationale: A + B + C = 5625
\inline B=\frac{1}{4}(A+C) \Rightarrow A+C =4B
\inline \therefore 4B + B = 5625
B = 1125
Also A + C = 4B = 4 x 1125 = 4500
Also \inline A=\frac{1}{2}(B+C)\Rightarrow B+C= 2A
B = 2A - C
\inline \therefore 2A - C = 1125
Now solving A+C = 4500 and 2A-C = 1125
Then A = 1875 and C = 2625
\inline \therefore A-B = 1875 - 1125 = Rs. 750
Answer:D
Answer: (D) 750
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer?
(A) 2388
(B) 2799
(C) 2877
(D) 4266
(E) 2881
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266.Answer:D
Answer: (D) 4266
Question: A library has an average of 425 visitors on Sundays and 325 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
(A) 140
(B) 240
(C) 260
(D) 280
(E) 340
Rationale: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (415 * 5 + 325 * 25) / 30 = 10200/30 = 340
Answer: E) 340
Answer: (E) 340
Question: A dog breeder would like to make the largest profit off of his latest litter of puppies. Puppies with more than 4 spots sell for more money. The last litter had 10 puppies; 6 had 5 spots, 3 had 4 spots, and 1 had 2 spots. What % of puppies can the dog breeder expect to sell for a greater profit?
(A) 90 %
(B) 65 %
(C) 50 %
(D) 85 %
(E) 80 %
Rationale: Number of dogs with profitable spots = (6 + 3)
= 6 + 3
= 9
Now, we need to calculate 9 is what percent of 10.
=> 9/10 * 100 = 90 %
A
Answer: (A) 90 %
Question: A secret can be told to only 2 persons in 3 minutes. Each person in turn tells 2 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way?
(A) 1024
(B) 2046
(C) 512
(D) 4096
(E) 5096
Rationale: 2^1 + 2^2 + 2^3 + 2^4 + ..............+2^10 = 2(2^10 - 1)/(2-1)
= 2*1023 = 2046
ANSWER:B
Answer: (B) 2046
Question: Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 324 grams of compound X?
(A) 54
(B) 162
(C) 250
(D) 270
(E) 322
Rationale: total number of fractions =2+10=12
element B constitutes =10 out of 12 parts of X
So in 324 gms of X have 324*10/12=270 gms of B
and 324-270=54 gms of A.
cross check:- A/B = 54/270 =2/10 (as given)
Ans D
Answer: (D) 270
Question: Two trains of equal lengths take 10 sec and 12 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 22
(B) 12
(C) 77
(D) 99
(E) 11
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/12 = 10 m/sec.
Relative speed = 12 + 10 = 22 m/sec.
Required time = (120 + 120)/22 = 11 sec.
Answer: E
Answer: (E) 11
Question: What is the median from the below series 90, 90, 93, 88, 95, 88, 97, 87, and 98
(A) 80
(B) 85
(C) 90
(D) 97
(E) 100
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 90, 93, 95, 96, 98
The median quiz score was 90. (Four quiz scores were higher than 90 and four were lower.)
C
Answer: (C) 90
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 10 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 135%
(D) 124.2%
(E) 138%
Rationale: the profit 0f 2009 in terms of 2008 = 0.9*15/10*100=135%
C
Answer: (C) 135%
Question: A train 110 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) 7
(B) 6
(C) 8
(D) 9
(E) 2
Rationale: 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 = [110 * 3/55] sec = 6 sec
Answer: B
Answer: (B) 6
Question: A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers?
(A) 5hr
(B) 6hr 30min
(C) 8hr 10min
(D) 7hr
(E) 9hr
Rationale: speed of man = 20km/hr
number of rests = (120/30)-1 = 3
time taken for the man = (120/20)+3*(20/60) = 7 hr
Answer is D
Answer: (D) 7hr
Question: What is the difference between the local values of 2 in the number 52402?
(A) 2992
(B) 2997
(C) 2877
(D) 2077
(E) 1998
Rationale: Explanation:
2000 â€“ 2 = 1998
Answer:E
Answer: (E) 1998
Question: At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts?
(A) 18
(B) 30
(C) 42
(D) 68
(E) 70
Rationale: the correct method
total = 300..
70% of 300 = 210 got gifts..
90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females..
But 40% females brought gift, so 60% did not get it..
so 60% = 45, 100%= 45*100/60= 75..
ans 40% of 75 =30
B
Answer: (B) 30
Question: What is the positive difference between the sum of the squares of the first 6 positive integers and the sum of the prime numbers between the first square and fourth square?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 50
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 +4^2+5^2+6^2 = 91
the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13=41.
So the difference between 41 and 91 is 50.
So the answer is (E).
Answer: (E) 50
Question: The sum of three numbers is 147. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
(A) 20
(B) 30
(C) 38
(D) 45
(E) None of these
Rationale: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 147
or 49x = 147 or x = 3
⇒ Second number = 15x = 15 × 3 = 45
Answer D
Answer: (D) 45
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 80 with him, what was the average amount with the group before his joining the group?
(A) s.12
(B) s.10
(C) s.15
(D) s.29
(E) s.19
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 80. So, the amount with remaining 6 people = 140 - 80 = Rs. 60
The average amount with them = 60/6
= Rs.10.
Answer:B
Answer: (B) s.10
Question: Raman mixed 54 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) 129
(B) 287
(C) 196
(D) 188
(E) 112
Rationale: Explanation:
CP per kg of mixture = [54(150) + 36(125)]/(54 + 36) = Rs. 140
SP = CP[(100 + profit%)/100]
= 140 * [(100 + 40)/100] = Rs. 196.
Answer:C
Answer: (C) 196
Question: The Guests at a football banquet consumed a total of 325 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
(A) 160
(B) 161
(C) 162
(D) 163
(E) 164
Rationale: To minimize one quantity maximize other.
162*2 (max possible amount of food a guest could consume) = 324 pounds, so there must be more than 162 guests, next integer is 163.
Answer: D.
Answer: (D) 163
Question: 1, 1, 3, 9, 11, 121,?
(A) 122
(B) 123
(C) 124
(D) 125
(E) 126
Rationale: 1^2 = 1 ......... 1+2 = 3
3^2 = 9 ....... 9+2 = 11
11^2 = 121 ...... 121+2 = 123
ANSWER:B
Answer: (B) 123
Question: A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number K is
(A) 74
(B) K=75
(C) K=175
(D) K=680
(E) 690
Rationale: I solved this question by plugging in numbers from the answer choices.
A.) 74
Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.
B.) 75
I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.
15-7 = 8 so I know the correct answer isB
Answer: (B) K=75
Question: If a and b are each greater than x and y, which of the following must be true?
I. ab > xy
II. a + b > x + y
III. |a| + |b| > |x| + |y|
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III
Rationale: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.
II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.
III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.
Answer: B.
Answer: (B) II only
Question: A train leaves Delhi at 9 a.m. at a speed of 35 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
(A) 229
(B) 288
(C) 600
(D) 888
(E) 1400
Rationale: D = 35 * 5 = 175
RS = 40 – 35 = 5
T = 175/5 = 35
D = 40 * 35 = 1400 km
Answer: E
Answer: (E) 1400
Question: How many zeros does 1000! end with?
(A) 20o
(B) 24o
(C) 249
(D) 30o
(E) 325
Rationale: According to above 1000! has 1000/5+1000/25+1000/125+1000/625=200+40+8+1=249 trailing zeros.
Answer: C
Answer: (C) 249
Question: A shopkeeper purchased 77 kg of potatoes for Rs. 539 and sold the whole lot at the rate of Rs. 8.50 per kg. What will be his gain percent?
(A) 18 1/9 %
(B) 28 9/3 %
(C) 28 1/3 %
(D) 32 1/3 %
(E) 21 3/7 %
Rationale: C.P. of 1 kg = 539/77 = Rs. 7S.P. of 1 kg = Rs. 8.50Gain % = 1.50/7 * 100 = 150/7 = 21 3/7 %Answer: E
Answer: (E) 21 3/7 %
Question: In a competitive examination in batch A, 8% candidates got selected from the total appeared candidates. batch B had an equal number of candidates appeared and 12% candidates got selected with 50 more candidates got selected than A. What was the number of candidates appeared from each batch?
(A) 1200
(B) 650
(C) 281
(D) 587
(E) 5000
Rationale: Batch A and Batch B had an equal number of candidates appeared.
In Batch A, 8% candidates got selected from the total appeared candidates
In Batch B, 12% candidates got selected from the total appeared candidates
But in Batch B, 50 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 50
=> total appeared candidates in Batch B = 50 x 100 = 5000
=> total appeared candidates in Batch A = total appeared candidates in Batch B = 5000
Answer : E
Answer: (E) 5000
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 4:5, find his marks in Science?
(A) 10.9
(B) 20.9
(C) 30.9
(D) 35
(E) 45
Rationale: S:E = 1:3
E:M = 4:5
------------
S:E:M = 4:12:15
4/31 * 162 = 20.9
ANSWER:B
Answer: (B) 20.9
Question: A group of 4 doctors and 2 nurses recently frequented the Lolly's Restaurant. The total bill for the meal, including 20% gratuity, came to $1440. On average, how much did the meal of each individual cost before gratuity?
(A) $160
(B) $60
(C) $200
(D) $80
(E) $55
Rationale: 4 doctors and 2 nurses - so total 6 people
The bill $1440 includes 20% gratuity... so the actual cost of dinner was $1200
Now, the cost per person will be $1200/6 which is $200
Option C
Answer: (C) $200
Question: If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions W represents the final price of the item?
(A) W=(10,000z + 100z(x – y) – xyz)/10,000
(B) W=(10,000z + 100z(y – x) – xyz)/10,000
(C) W=(100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: -A-
z=Original Price
x=MU
y= MD
New price with MU:
z(x/100+1)
New price with MD:
z[(x/100+1)(-y/100+1)]
Solvingâ€¦
=z[((x+100)/100)((-y+100)/100)]
=z(x100-xy+10000-100y)/10000
=(zx100-xyz+10000z-100yz)/10000 --> similar to A
Answer: (A) W=(10,000z + 100z(x – y) – xyz)/10,000
Question: A scale 10 ft. 5 inches long is divided into 5 equal parts. Find the length of each part.
(A) 25 inches
(B) 77 inches
(C) 66 inches
(D) 97 inches
(E) 66 inches
Rationale: Explanation:
Total length of scale in inches = (10*12) + 5 = 125 inches
Length of each of the 5 parts = 125/5 = 25 inches
ANSWER:A
Answer: (A) 25 inches
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 6600 ?
(A) 11
(B) 13
(C) 14
(D) 18
(E) 10
Rationale: Required difference = [3 ½ % of Rs.6600] – [3 1/3 % of Rs.6600]
= [(7/20-(10/3)]% of Rs.6600 =1/6 % of Rs.6600
= Rs. [(1/6)8(1/100)*6600] = Rs. 11.
Answer is A.
Answer: (A) 11
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda spends 70% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?
(A) 1/7 m
(B) 1/3 m
(C) 1/4 m
(D) 1/5 m
(E) 1/6 m
Rationale: After the final transaction:
Angela received $(m-n) for t hours;
Linda received $(m+n) for 1.5t hours;
We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/7.
Answer: A.
Answer: (A) 1/7 m
Question: A room contains 150 people, 12 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Say group of x people left the room.
# of women in the room was 0.12*150=18;
# of women in the group that left 0.15x;
# of women in the room after the group left it is 0.1(150-x);
So, 18-0.15x= 0.1(150-x) --> x=60.
Answer: C.
Answer: (C) 60
Question: Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
(A) 66
(B) 70
(C) 72
(D) 75
(E) 78
Rationale: Let the distance one way be x
Time from home to work = x/75
Time from work to home = x/105
Total time = 2 hrs
(x/75) + (x/105)= 2
Solving for x, we get x = 175/2
Time from home to work in minutes= (175/2)*60/75 = 70 minutes
Ans= B
Answer: (B) 70
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
(A) 50 kmph
(B) 520 kmph
(C) 56 kmph
(D) 59 kmph
(E) 53 kmph
Rationale: A
50 kmph
Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.
Answer: (A) 50 kmph