mathewhe/aqua_rat huggingface dataset:
Question: The simple interest on a sum of money will be Rs.700 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 2261
(B) 2888
(C) 1400
(D) 2699
(E) 2771
Rationale: P --- 10 ---- 700
P --- 5 ----- 350
3P --- 5 ----- 1050
------
=> 1400
Answer: C
Answer: (C) 1400
Question: The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 67 kmph
(C) 22 kmph
(D) 20 kmph
(E) 12 kmph
Rationale: Speed of the boat in still water
= (40+80)/2
= 60 kmph. Speed of the stream
= (80-40)/2
= 20 kmph.
Answer:D
Answer: (D) 20 kmph
Question: In a factory, there are 60% technicians and 100% non-technicians. If the 60% of the technicians and 100% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 62%
(B) 57%
(C) 52%
(D) 85%
(E) 42%
Rationale: Total = 160
T= 60 NT= 100
60*(100/100)=37.5 100*(60/100)=37.5
37.5 + 37.5 = 75=> 160 - 75 = 85%
Answer:D
Answer: (D) 85%
Question: 4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are
(A) 4
(B) 8
(C) 12
(D) 16
(E) 18
Rationale: Explanation :
Since the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways.
Answer : C
Answer: (C) 12
Question: If BASKET is coded as 116,then COLOUR is coded as,
(A) 158
(B) 168
(C) 178
(D) 188
(E) 198
Rationale: NUMBER THE ALPHABETS
B=2, A=1, S=19, K=11, E=5, T=20
BASKET = 116
2(B+A+S+K+E+T) ==>2(2+1+19+11+5+20) = 2(58) = 116
Similarly C=3, O=15, L=12, O=15, U=21, R=18
2(C+O+L+O+U+R) = 2(3+15+12+15+21+18) = 2(84) = 168
ANSWER:B
Answer: (B) 168
Question: An article is bought for Rs.685 and sold for Rs.900, find the gain percent?
(A) 30 1/3%
(B) 33 1/3%
(C) 31 53/137%
(D) 35 1/3%
(E) 29 1/3%
Rationale: C
31 53/137%
685 ---- 215
100 ---- ? => 31 53/137%
Answer: (C) 31 53/137%
Question: For the set {2, 2, 3, 3, 4, 4, 5, 5,6,6 x}, which of the following values of x will most increase the standard deviation?
(A) 1
(B) 2
(C) (-3)^2
(D) 4
(E) 5
Rationale: Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4
Step 2, For each number: subtract the Mean and square the result =
(1-4)^2=(-3)^2
(2-4)^2=(-2)^2
(3-4)^2 =(-1)^2
(4-4)^2=(0)^2
(5-4)^2=(1)^2
Clearly (1-3.5)^2=(-2.5)^2 will give you the greatest value among all the other options.
Hence C
Answer: (C) (-3)^2
Question: If the number of boys in a class are 8 times the number of girls, which value can be the total number of students?
(A) A - 42
(B) B - 45
(C) C - 41
(D) D - 40
(E) E - 39
Rationale: Let the number of girls = x and the number of boys = 8x Then, total number of students = x + 8x = 9x i.e., the total number of students must be a multiple of 9 From the given choices, only 45 cannot be a multiple of 9. Hence, 45 is the total number of students. Answer is B.
Answer: (B) B - 45
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 4 1/2 percent?
(A) 263
(B) 500
(C) 388.9
(D) 368
(E) 339
Rationale: 70 = (P*4*9/2)/100
P = 388.9
Answer: C
Answer: (C) 388.9
Question: Three sets of 80, 50 and 60 students appeared for an examination and the pass percentage was 100, 90 and 50 respectively. the pass percentage of the whole set is
(A) 86.57%
(B) 89.57%
(C) 82.57%
(D) 81.97%
(E) 81.57%
Rationale: Explanation:
total passed student =80+45+30=155
155 is 81.57% of 190
ANSWER:E
Answer: (E) 81.57%
Question: A driver took a trip consisting of three segments at three different speeds. The driver drove a distance of (5D) at a speed of (2V), then a distance of (10D) at a speed of (3V), then a distance of D at a speed of (6V). In terms of D and V, what was the total time of the trip?
(A) 3D/V
(B) 4D/V
(C) 5D/V
(D) 6D/V
(E) 7D/V
Rationale: The total time of the trip was:
5D/2V + 10D/3V + D/6V =
30D/12V + 40D/12V + 2D/12V =
72D/12V = 6D/V
The answer is D.
Answer: (D) 6D/V
Question: The average height of 20 students in a class was calculated as 175 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 111 cm. What was the actual average height of the students in the class?
(A) 174 cm
(B) 173 cm
(C) 172 cm
(D) 171 cm
(E) 170 cm
Rationale: The total height was 40 cm too much.
The average height should be reduced by 40 cm/20 = 2 cm
The answer is B.
Answer: (B) 173 cm
Question: A Man can row upstream at 85kmph and downward stream at 47 kmph. Find Man's rate of the current
(A) 19km/hr
(B) 20km/hr
(C) 65km/hr
(D) 2.8km/hr
(E) 4.4km/hr
Rationale: Rate of the current=1/2(85-47)km/hr
=19km/hr
correct option is :A
Answer: (A) 19km/hr
Question: The ratio of three numbers is 1:2:3 and the sum of their squares is 2744. The sum of the numbers is?
(A) 10
(B) 12
(C) 15
(D) 14
(E) 9
Rationale: Let the numbers be x,2x,3x
then, x^2+4x^2+9x^2 = 2744
14x^2 = 2744
x^2 = 196
x=14
Answer is D
Answer: (D) 14
Question: Reena is twice as old as Sunita. Three years ago, she was three times as old as Sunita. How old is Reena now ?
(A) 14 years
(B) 6 years
(C) 12 years
(D) 18 years
(E) 16 years
Rationale: Let Sunita's present age = x years
Then Reena present age = 2x years
Three years ago
(2x-3) = 3(x-3)
2x - 3 = 3x - 9
or x = 6
Reena age = 2x = 2*6 = 12 year.
Answer: Option C
Answer: (C) 12 years
Question: There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
(A) 90
(B) 120
(C) 675
(D) 180
(E) 200
Rationale: Number of ways of selecting 2 fiction books = 10C2
Number of ways of selecting 2 non fiction books = 6C2
10C2 * 6C2 = 45 * 15 = 675
Answer: C
Answer: (C) 675
Question: Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
answer :C
Answer: (C) 4
Question: Two bottles A and B contain diluted ammonium nitric acid. In bottle A, the amount of water is double the amount of acid while in bottle B, the amount of acid is 3 times that of water. How much mixture Should be taken from each bottle in order to prepare 5 litres of diluted sulphuric acid containing equal amount of acid and water?
(A) 1, 4
(B) Required ratio= 3, 2
(C) 2, 3
(D) 4, 1
(E) 1,5
Rationale: A B
Acid water Acid water
1 : 2 3 : 1
Acid=1/3 Acid=3/4
Mixture=Acid:Water=1:1 Required acid=1/2
Now,Required ratio=(1/4): (1/6)=3:2
So the required quantity is 3 and 2 litres respectively.
ANSWER:B
Answer: (B) Required ratio= 3, 2
Question: A man purchases a cow for Rs.3000 and sold it on the same day allowing the buyer a credit of 2 years. If the buyer will pay Rs.3600 after 2 year at a rate of simple interest 50/7 % per annum, then the man has a gain of
(A) Rs 181.43
(B) Rs 171.43
(C) Rs 191.43
(D) Rs 161.43
(E) Rs 151.43
Rationale: value of Rs3000 after 2 years at 50/7 % S.I will be = 3000 + (3000*2*50/7)/100 = 3000 + 428.57
= 3428.57
therefore C.P of article after 2 years will be Rs 3428.57
but the buyer pays Rs 3600
therefore gain = 3600-3428.57 = Rs 171.43
ANSWER:B
Answer: (B) Rs 171.43
Question: In the simple subtraction problem below, some single digits (not necessarily distinct) are replaced by letters. Find the value of 2*A + 2*B + 4*C*D.
A9C5
-	2B79
--------------
633D
(A) 50
(B) 52
(C) 66
(D) 48
(E) 46
Rationale: A9C5
-2B79
----------
6336 since,15-9=6. from there,D=6 and solving all,we get A=8,B=5,C=1.
So 2*8+2*5+4*1*6=50
ANSWER:A
Answer: (A) 50
Question: A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum B of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?
(A)  5
(B)  7
(C)  9
(D)  10
(E)  14
Rationale: Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum B of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D
Answer: (D)  10
Question: Right triangle RST can be constructed in the xy-plane such that RS is perpendicular to the y-axis and the right angle is at R. The x and y-coordinates of R, S, and T are to be nonzero integers that satisfy the inequalities −3 ≤ x ≤ 4 and −7 ≤ y ≤ 3. Given these restrictions , how many different triangles can be constructed?
(A) 3780
(B) 4200
(C) 4900
(D) 6160
(E) 7744
Rationale: −3 ≤ x ≤ 4 and −7 ≤ y ≤ 3 gives a rectangle with 8*11 dimensions (8 horizontal and 11 vertical dots). We are given that RS is parallel to x-axis, RT is parallel to y-axis and the right angle is at R.
Choose the (x,y) coordinates for vertex R: 7C1*10C1 (we are told that coordinates of R, S, and T must be nonzero integers, so we are choosing from 7 and 10 instead of 8 and 11 because we should exclude 0);
Choose the x coordinate for vertex S (as y coordinate is fixed by R): 6C1, (7-1=6 as 1 horizontal dot is already occupied by R);
Choose the y coordinate for vertex T (as x coordinate is fixed by R): 9C1, (10-1=9 as 1 vertical dot is already occupied by B).
7C1*10C1*6C1*9C1=3,780.
Answer: A.
Answer: (A) 3780
Question: What is the smallest no. that should be added to 236 to make it exactly divisible by 9?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 2+3+6=11, the next multiple of 9 is 18.
7 must be added to 236 to make it divisible by 9
D
Answer: (D) 7
Question: In the first week of the Year, ancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that ancy saved during the 52 weeks?
(A) $1,326
(B) $1,352
(C) $1,378
(D) $2,652
(E) $2,756
Rationale: In the first week of the Year, ancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Answer: (C) $1,378
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
(A) 35.55 km/hr
(B) 36 km/hr
(C) 71 km/hr
(D) 71.11 km/hr
(E) 70 km/hr
Rationale: Total time taken =((160/64)+(160/80))hrs=9/2hrs.
Average speed =(320 x2/9)km/hr= 71.11 km/hr.
ANSWER D
Answer: (D) 71.11 km/hr
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.60 per kg. What will be his gain percent?
(A) 8 1/7 %
(B) 2 1/3 %
(C) 10 %
(D) 8 1/8 %
(E) 8 1/9 %
Rationale: C.P. of 1 kg = 420/70 = Rs. 6
S.P. of 1 kg = Rs. 6.60
Gain % = 0.60/6 * 100 = 10
= 10 %
Answer:C
Answer: (C) 10 %
Question: A trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent?
(A) No profit No loss
(B) 4% profit
(C) 2% loss
(D) 2% profit
(E) None of these
Rationale: Let CP of an article = RS. 100
MP= Rs. 120
Discount = 20%
SP = M[(100 - d%)/100] = 120(80/100) = Rs. 96
Clearly, the trader gets 4% loss.
ANSWER:E
Answer: (E) None of these
Question: In how many different ways can 6 identical blue pants and 6 identical red pants be shared among 12 children such that each child receives a pant?
(A) 47900
(B) 4790016
(C) 479001
(D) 47900160
(E) 479001600
Rationale: GGG RRR
Therefore total number of ways is
12! but there are two groups of 3 identical things.
Therefore total number of "different" ways is
12!/ (6!) (6!) = 479001600 ANS:E
Answer: (E) 479001600
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:6
(B) 17:3
(C) 17:1
(D) 17:9
(E) 17:4
Rationale: P:Q = 85000 : 15000
= 17:3.
Answer:B
Answer: (B) 17:3
Question: Mamuni went to the movies nine days ago. She goes to the movies only on Thursday. What day of the week is today?
(A) Sunday
(B) Tuesday
(C) Thursday
(D) Saturday
(E) Friday
Rationale: Clearly, Nine days ago, it was Thursday.
Today is Saturday
ANSWER:D
Answer: (D) Saturday
Question: Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined Bobby had:
(A) A profit of $10
(B) A profit of $8
(C) A loss of $8
(D) A loss of $10
(E) Neither a profit nor a loss
Rationale: Cost of the first stock: 96/1.2=80, so profit from it 96-80=16
Cost of the second stock: 96/0.8=120, so loss from it 96-120=-24
Overall loss 16-24=-8
Answer: C.
Answer: (C) A loss of $8
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/7
(B) 5/9
(C) 5/6
(D) 5/4
(E) 5/2
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9
Answer:B
Answer: (B) 5/9
Question: A train 125 m long passes a man, running at 9 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 11
(B) 50
(C) 88
(D) 65
(E) 54
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 9) km/hr. x - 9 = 45 ==> x
= 54 km/hr.
Answer:E
Answer: (E) 54
Question: If an object travels at three feet per second, how many feet does it travel in one hour?
(A) 3488
(B) 10800
(C) 12788
(D) 1800
(E) 2881
Rationale: Explanation:
If an object travels at 2 feet per second it covers 3x60 feet in one minute, and 3x60x60 feet in one hour.
Answer = 10800
Answer: B) 10800
Answer: (B) 10800
Question: In how many ways can 7 people, A, B, C, D, E, F, G be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
(A) 384
(B) 396
(C) 576
(D) 4944
(E) 696
Rationale: Number of total arrangements = 7!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
7! - (4!*2*2) = 5040 - (24*2*2) = 4944
Answer D
Answer: (D) 4944
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 18/67
(C) 18/78
(D) 18/33
(E) 18/28
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A
Answer: (A) 18/35
Question: a person purchased four cloth average price of cloth is 300.price of its three cloths are 350,400,200 respectively what will be the price of fourth cloth?
(A) 300
(B) 250
(C) 200
(D) 400
(E) 275
Rationale: sum of price of all cloth=300*4=1200
sum of price of three cloth=350+400+200=950
price of fourth cloth=1200-950=250
answer B
Answer: (B) 250
Question: Mrs. Mary. invested $36,000; part at 5%, and part at 8%. The total interest on the investment was $2,520. How much did she invest at each rate?
(A) x=$15,000, y =$30,000
(B) x=$16,000, y =$32,000
(C) x=$12,000, y =$24,000
(D) x=$5,000, y =$10,000
(E) x=$13,000, y =$26,000
Rationale: I approached this question like a mixture problem.
I don't like the wordingpartat 5% andpartat 8% because we have variables x and y in the answer choices and I have no idea which one is x or y.
Anyway here's how I did it.
0.05(x) + 0.08(y) = 0.07(x+y)
0.01(y) = 0.02(x)
y = 2x
Note: 0.07(x+y) because $2,520 is 7% of 36,000
In which answer choice is y = 2(x)
Answer C
Answer: (C) x=$12,000, y =$24,000
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $324 per week
36x =324
x =9
Correct Option : C. 9
Answer: (C) 9
Question: What is the difference between the compound interest on Rs.12000 at 30% p.a. for one year when compounded yearly and half yearly?
(A) 399
(B) 383
(C) 270
(D) 288
(E) 133
Rationale: When compounded annually, interest
= 12000[1 + 30/100]1 - 12000 = Rs.3600
When compounded semi-annually, interest
= 12000[1 + 15/100]2 - 12000 = Rs.3870
Required difference = 3870- 3600 = Rs.270
Answer: C
Answer: (C) 270
Question: Of three numbers, the third is twice the first and the second is 4 times the first. If their average is 77, the smallest of the three numbers is:
(A) 18
(B) 25
(C) 20
(D) 32
(E) 33
Rationale: Explanation:
Let first number be x.
So,2nd no. = 4x & 3rd no.=2x.
So,x+4x+2x=77 × 3 = 231
7x = 231
x = 231/7
Hence,smallest Number x=33
Answer: E
Answer: (E) 33
Question: A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
(A) 4 days
(B) 8 days
(C) 2 days
(D) 12 days
(E) 6 days
Rationale: Suppose A, B and C take x,	x/2 and x/3 days respectively to finish the work.
Then,1/x+ 2/x + 3/x = 1/2
6/x = 1/2
x = 12.
So, B takes (12/2) = 6 days to finish the work
ANSWER:E
Answer: (E) 6 days
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.48, find the sum of money?
(A) 288
(B) 262
(C) 246
(D) 205
(E) 267
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 48
41 ---- ? => Rs.246
Answer: C
Answer: (C) 246
Question: The ratio between the current age of A and B is 6:7. If B is 4 years old than A. What will be the ratio of the ages of A and B after 4 years?
(A) 7:8
(B) 8:9
(C) 4:6
(D) 4:8
(E) 5:8
Rationale: A
7:8
If A’s age and B’s age will be 6A years and 7A years correspondingly
Then, 7A – 6A = 4
A = 4
Needed ratio = (6A + 4) : (7A + 4)
= 28 : 32
= 7 : 8
Answer: (A) 7:8
Question: How many seconds does Sandy take to cover a distance of 700 meters, if Sandy runs at a speed of 18 km/hr?
(A) 100
(B) 120
(C) 140
(D) 160
(E) 180
Rationale: 18 km/hr = 18000 m / 3600 s = 5 m/s
time = 700 / 5 = 140 seconds
The answer is C.
Answer: (C) 140
Question: Company P had 15 percent more employees in December than it had in January. If Company P had 500 employees in December, how many employees did it have in January?
(A)  391
(B)  435
(C)  410
(D)  423
(E)  445
Rationale: D = number of employees in December
J = number of employees in January
J x 1.15 = D
J x 1.15 = 500
J = 500/1.15
J = 50,000/115 = 435
Thus B is the correct answer.
Answer: (B)  435
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 25 hours after they passed each other the ratio of the speeds of the two trains was
(A) 2:1
(B) 3:2
(C) 4:3
(D) 5:2
(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 = = 5 : 2. Answer: D
Answer: (D) 5:2
Question: Two-fifths of thirty per cent of one-fourth of a number is 15. What is 20 per cent of that number?
(A) 90
(B) 150
(C) 100
(D) 120
(E) None of these
Rationale: Let the number = x
2⁄5 × 30⁄100 × x⁄4 = 15
or x=15×5×100/2×30=500
20% of 500 = 100
Answer C
Answer: (C) 100
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?
(A) 13 kmph
(B) 15 kmph
(C) 12 kmph
(D) 16 kmph
(E) 18 kmph
Rationale: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Answer: (C) 12 kmph
Question: At the end of the day one market stall had 16 apples and 48 oranges left. Another market stall had 36 apples and 24 oranges left. What is the difference between the percentages of apples left in the two market stalls?
(A) 39%
(B) 37%
(C) 38%
(D) 35%
(E) 40%
Rationale: D
35%
First stall 16 out of 64= 25%.
Second stall 36 out of 60 = 60%.
Difference in percentages = 35%.
Answer: (D) 35%
Question: If 2^5, 3^3, and 14^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
(A) 26
(B) 39
(C) 42
(D) 65
(E) 168
Rationale: Here 156 has three two's
two three's
and one 14
rest of them must be in w
so w= 14*3*4 = 168
Smash E
Answer: (E) 168
Question: If a car went the first third of the distance at 60 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?
(A) 38 kmh
(B) 40 kmh
(C) 42 kmh
(D) 44 kmh
(E) 50 kmh
Rationale: Assume D/3 = 240 (this number is convenient because it is divisible by 60, 24 and 48)
So:
240 = 60*T1 = 4 hrs
240 = 24*T2 = 10 hrs
240 = 48*T3 = 5 hrs
T = T1 + T2 + T3 = 19 hrs
D = RT
(240*3) = R*19
R = 38
ANSWER: A
Answer: (A) 38 kmh
Question: A candidate appearing for an examination has to secure 35% marks to pass paper I. But he secured only 42 marks and failed by 23 marks. What is the maximum mark for paper I?
(A) 110
(B) 120
(C) 186
(D) 140
(E) 150
Rationale: he secured 42 marks nd fail by 23 marks so
total marks for pass the examinatn=65
let toal marks x
x*35/100=65
x=186
ANSWER:C
Answer: (C) 186
Question: A man swims downstream 42 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 2
(B) 8
(C) 9
(D) 6
(E) 10
Rationale: 42 --- 3 DS = 14
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (14 + 6)/2 =10
Answer: E
Answer: (E) 10
Question: Suppose you want to buy three loaves of bread that cost $2.25 each
and a jar of peanut butter that costs $2. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $14. How much money will you have left
over?
(A) $1.50
(B) $2.50
(C) $5.25
(D) $4.50
(E) $5.50
Rationale: The jelly is extra information. 14.00 â€“ 3 x 2.25 â€“ 2.00 =
14.00 â€“ 6.75 â€“ 2.00 = 5.25.
You have $5.25 left.
correct answer C
Answer: (C) $5.25