mathewhe/aqua_rat huggingface dataset:
Question: When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 70% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed, then
(A) Jack picks double the amount of olives Mac picks
(B) Mac picks 10 pounds more than Jack
(C) Jack picks 10 pounds more than Mac
(D) Mac picks 5 more pounds than Jack
(E) Jack picks 5 more pounds than Mac
Rationale: Let's say Jack's regular speed is J olives/hr and Mac's regular speed is M olives/hr
Given:
2*3J = 10 + 5*(4/5)M
3J = 5 + 2M
Question:if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed
Mac picks 2M and Jack picks 4*(3/4)J = 3J
They are asking you for the relation between 3J and 2M. You already know 3J = 5 + 2M
So Jack picks 10 pounds more olives than Mac.
B
Answer: (B) Mac picks 10 pounds more than Jack
Question: 10 litres of water is added to 50 litres of a solution containing 20% of alcohol in water . What is the strength of alcohol in the solution now ?
(A) 20%
(B) 16 2/3 %
(C) 12 1/2 %
(D) 33 1/3 %
(E) 23 1/3 %
Rationale: Quantity of alcohol in 50 litres = 50*20/100 =10
strength in 60 litre solution = 10/60*100 = 100/6 = 16 2/3
ANSWER:B
Answer: (B) 16 2/3 %
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present
(A) 42
(B) 22
(C) 20
(D) 40
(E) 26
Rationale: Let the mother's present age be X years.
Then, the person's present age = 2/5 X years.
THEREFORE (2/5 X + 8) = 1/2 (X+8)
2(2X + 40) = 5(X + 8)
X = 40
ANSWER:D
Answer: (D) 40
Question: Apple, orange, mango. Mango + apple=12. Mango + orange=10.
Mango +Apple + orange=38. Calculate the no of mango?
(A) -8
(B) -9
(C) -10
(D) -12
(E) -16
Rationale: Mango + apple=12.............(A)
Mango + orange=10..........(B)
Adding A and B
2 Mango + Apple +orange = 22
but
Mango +Apple + orange=38.... given
which is not possible.
In this case, no of mangoes is negative ( -16)
ANSWER:D
Answer: (D) -12
Question: The value of x+2+xx -x(x+x) when x = 2 is:
(A) 5
(B) 4
(C) 0
(D) 3
(E) 6
Rationale: x+2+xx -x(x+x)
Put the value of x = 2 in the above expression we get,
2+2+2*2 - 2(2+2)
= 2+2+4-8
= 0
Answer C
Answer: (C) 0
Question: A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. !find the share of B.
(A) 225
(B) 500
(C) 75
(D) 800
(E) None 0of them
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (600 *4/8) = Rs.300, B's share = Rs. (600 *3/8) = Rs. 225.
C's share = Rs. [600 - (300 + 225») = Rs. 75.
Answer is A
Answer: (A) 225
Question: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: Cashews /peanuts = (Mean price - peanuts price)/(Cashew price - Mean price) = (2.5-1.5)/(4-2.5) = 2/3
Cashew = (2/5)*100 = 40 Kg
Answer is A.
Answer: (A) 40
Question: By selling 88 pens, a trader gains the cost of 22 pens. Find his gain percentage?
(A) 25%
(B) 26%
(C) 27%
(D) 28%
(E) 29%
Rationale: Let the CP of each pen be Rs. 1.
CP of 88 pens = Rs. 88
Profit = Cost of 22 pens = Rs. 22
Profit% = 22/88 * 100 = 25%
Answer:A
Answer: (A) 25%
Question: What is the value of x^2yz − xyz^2, if x = − 2, y = 1, and z = 4?
(A)  20
(B)  24
(C)  30
(D)  32
(E)  48
Rationale: 4*1*4 -(- 2*1*16)
=16+32 = 48
Ans: E
Answer: (E)  48
Question: 10 women can complete a work in 8 days and 10 children take 12 days to complete the work. How many days will 6 women and 3 children together take to complete the work?
(A) 7
(B) 10
(C) 8
(D) 9
(E) 11
Rationale: Explanation:
1 women’s 1 day’s work = 1/8/10 = 1/80
1 child’s 1 day’s work = 1/12/10 = 1/120
6 women’s 1 day’s work = 1/80 × 6 = 3/40
3 children’s 1 day’s work = 1/120 × 3 = 1/40
6 women’s + 3 children’s 1 day’s work = 3 /40 + 1/40 = 1/10
Therefore, they will finish the whole work in 10 days.
Answer: Option B
Answer: (B) 10
Question: In a division sum, the remainder is 4 and the divisor is 2 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:
(A) 72
(B) 90
(C) 100
(D) 110
(E) 120
Rationale: Diver = (4*3)+2 = 14
2* Quotient = 14
Quotient = 7
Dividend = (Divisor * Quotient) + Remainder
Dividend = (14 * 7) + 2 = 100
C
Answer: (C) 100
Question: A ladies hostel had provision of food for 150 women for 25 days. After 5 days, 25 women left the hostel. The number of days for which the remaining food will last is:
(A) 64
(B) 50
(C) 28
(D) 26
(E) 24
Rationale: Explanation :
After 5 days : 150 women had food for 20 days.
Suppose 125 women had food for x days.
Now, Less women, More days (Indirect Proportion)
125 : 150 :: 20 : x
=> 125 x x = 150 x 20
=> x = 150 x 20 / 125
=> x = 24.
Answer : E
Answer: (E) 24
Question: You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 2 baseball cards. How many baseball cards do you have at the end?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Solution
Start with 16 baseball cards.
John takes 3 baseball cards from you: 16 - 2 = 14 baseball cards.
So you have 14 at the end.
Correct answer : D
Answer: (D) 14
Question: A certain rectangular window is (2/5) times as long as it is wide. If its perimeter is 28 feet, what are its dimensions in terms of length by width?
(A) 12 by 2
(B) 11 by 3
(C) 10.5 by 3.5
(D) 10 by 4
(E) 9 by 3
Rationale: 2x+2y=28
x+y=14
x+(2/5)x=14
1.4x=14
x=10
Answer D
Answer: (D) 10 by 4
Question: A certain fruit stand sold cherry for $0.70 each and guava for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7.
63 is a direct multiple of 7, however in this case there won't be any bananas. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7
A
Answer: (A) 11
Question: A train covers a distance of 9 km in 6 min. If it takes 5 sec to pass a telegraph post, then the length of the train is?
(A) 100
(B) 105
(C) 110
(D) 120
(E) 125
Rationale: Speed = (9/6 * 60) km/hr = (90 * 5/18) m/sec = 25 m/sec.
Length of the train = 25 * 5 = 125 m.
Answer: Option E
Answer: (E) 125
Question: How many natural numbers that are less than 10,000 can be formed using the digits 0, 1, 2, 3, 4, 6, 7 & 8?
(A) 5000
(B) 4096
(C) 6560
(D) 4095
(E) 8000
Rationale: Solution:
We are missing digits 5 and 9 in the question. So we have 8 digits for each position (ones,tens,hundreds,thousands).
The numbers that can be constructed using 8 digits in 4 positions = (8 x 8 x 8 x 8) - 1 (To disregard the case 0000)
= 4096 - 1
= 4095
If you have use 10 digits (0 thru 9), you have (10 x 10 x 10 x 10) - 1 = 9999 numbers.
Answer D.
Answer: (D) 4095
Question: A woman has three blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
(A) 8
(B) 12
(C) 16
(D) 17
(E) 18
Rationale: total ways = 3*3*2=18..
now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..
the ways in which the pink blouse and green skirt are together=1*1*2=2..
total ways =18-2=16..
ANSWER:C
Answer: (C) 16
Question: Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 4 ?
(A) 1/3
(B) 1/2
(C) 1/6
(D) 1/5
(E) 1/4
Rationale: (6,2) (2,6) (5,3) (3,5) (4,4) – only 5 possible scenarios for sum to be 8. One from this 5 has already happened.
From this five cases, only in one we have 4. So, the probability is 1 chances out of 5 that the one that occurred had 4: P=1/5.
Answer: D.
Answer: (D) 1/5
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 54.Find the number of notes of Rs.50 denomination.
(A) 15
(B) 21
(C) 37
(D) 19
(E) 21
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 54 - X
Now,
50*X + 500 * (54 - X) = 10350
50X + 27000 - 500X = 10350
- 450X = - 16650
X = 37.
No. of 50 rupees note = 37.
Answer: Option C
Answer: (C) 37
Question: On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is?
(A) 8
(B) 10
(C) 12
(D) 16
(E) 18
Rationale: Clearly, (2272 - 875) = 1397, is exactly divisible by N.
Now, 1397 = 11 x 127
The required 3-digit number is 127, the sum of whose digits is 10
Option B
Answer: (B) 10
Question: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 45% nuts, what percent of the combined mixture is dried fruit?
(A) 25%
(B) 30%
(C) 35%
(D) 40%
(E) 45%
Rationale: 45% is 15%-points above 30% and 15%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 1:1.
1/2*70% = 35%
The answer is C.
Answer: (C) 35%
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 22 seconds, what is the ratio of their speeds?
(A) 1:1
(B) 3:1
(C) 2:3
(D) 3:2
(E) 3:4
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 22 s
= (27x + 17 y)/(x+y) = 22
= (27x + 17 y)/ = 22(x+y)
= 5x = 5y
=x/y = 5/5 = 1/1 i.e 1:1
Answer :A
Answer: (A) 1:1
Question: Aamir saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?
(A) 29998
(B) 77827
(C) 26772
(D) 12800
(E) 21212
Rationale: Let the monthly salary of Aamir be Rs. x.
68% of x = 27200
=> x = (27200 * 100)/68 = 40000
His savings = 32/100 * 40000 = 12800.
Answer: D
Answer: (D) 12800
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is?
(A) 8118
(B) 8127
(C) 8618
(D) 8436
(E) 8128
Rationale: A = 7500(26/25)3
= 8436
Answer: D
Answer: (D) 8436
Question: Jacob is now 12 years younger than Michael. If 5 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
(A)  3
(B)  7
(C)  11
(D)  21
(E)  25
Rationale: Jacob=x years, Mike=x+12 years
5 years from now,
2(x+5)=x+17
2x+10=x+17
x=7
x+4=11 years
Answer C
Answer: (C)  11
Question: Three numbers are in the ratio 4:2:5 and their H.C.F is 12. The numbers are:
(A) 4, 2, 5
(B) 5, 10, 15
(C) 10, 20, 30
(D) 48, 24, 60.
(E) 12, 24, 60
Rationale: Let the required numbers be 4x, 2x and 5x. Then, their H.C.F = x. So, x = 12.
The numbers are 48, 24, 60.
ANSWER:D
Answer: (D) 48, 24, 60.
Question: Pencils, Pens and Exercise books in a shop are in the ratio of 14: 4 : 3. If there are 140 pencils, the number of exercise books in the shop is:
(A) 30
(B) 27
(C) 35
(D) 33
(E) 37
Rationale: Explanation :
Let Pencils = 14x, Pens = 4x & Exercise books = 3x.
Now, 14x = 140
hence x = 10
Number of exercise books = 3x = 30
Answer : A
Answer: (A) 30
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
(A) 2205
(B) 1978
(C) 2834
(D) 2827
(E) 2781
Rationale: A = 2000(21/20)2
= 2205
Answer: A
Answer: (A) 2205
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 8
(C) 9
(D) 2
(E) 9
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer:A
Answer: (A) 4
Question: The last time Meena bought Diwali cards, he found that the three types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50 each. As Meena wanted 30 cards, she took ten each of three cards , putting down the exact number of 10 rupees notes on the counter payment. How many notes did Meena give?
(A) 5
(B) 15
(C) 10
(D) 12
(E) 13
Rationale: Explanation :
Let the three cards be a, b ,c . 'x' be the number of notes.
Then, according to the question,
=> 10a + 10b + 10c = 10*x.
=> a + b + c= x . -----------------------------(i)
Since, a + b +c= 3.5 + 4.5 +2.0= x
x =10
Answer : C
Answer: (C) 10
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 15 seconds. What is the length of the platform in meters?
(A) 240 meters
(B) 360 meters
(C) 300 meters
(D) 600 meters
(E) Cannot be determined
Rationale: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 15 * 20 = 300 = Length of train
Length of platform = 600 - 300 = 300
Answer: C
Answer: (C) 300 meters
Question: A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 2, what is the smallest possible total number of tokens in the jar?
(A)  9
(B)  12
(C)  15
(D)  18
(E)  21
Rationale: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)
i.e. Red*White = Blue*Total Coins
Let, Red = 3a
White = 3b
Blue = 3c
Total Coins = 3(a+b+c)
i.e. 3a * 3b = 3c*3(a+b+c)
i.e. a*b = c*(a+b+c)
For smallest values of a, b and c
2*3 = 1*(1+2+3)
i.e. Minimum Total Coins = 3*(1+2+3) = 18
Answer: Option B
Answer: (B)  12
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 5 on it exactly once?
(A) 9/100
(B) 1/10
(C) 18/100
(D) 19/100
(E) 1/5
Rationale: Probability = No of balls with exactly one 1 / total number of balls
= {5,15,25,35,45,50,51,52,53,54,56 to 59,65,75,85,95}/100
= 18/100
Answer is C
Answer: (C) 18/100
Question: Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = 2
(II) y = 6
(III) x + y = 0
(A) II &III
(B) III
(C) I and II only
(D) I
(E) II
Rationale: y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
E
Answer: (E) II
Question: Ravi and Kavi start a business by investing ₹ 8000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year.
(A) 2 : 9
(B) 5 : 9
(C) 7 : 9
(D) 1 : 9
(E) 3 : 9
Rationale: Ratio of profit = Ratio of investments
= 8000 : 72000 = 1 : 9
Answer : D
Answer: (D) 1 : 9
Question: 33 1/3% OF 360?
(A) 80
(B) 90
(C) 110
(D) 120
(E) 130
Rationale: 33 1/3 % = 1/3
1/3 × 360 = 120
D)
Answer: (D) 120
Question: Find the average of first 97 natural numbers.
(A) 47
(B) 37
(C) 48
(D) 49
(E) 49.5
Rationale: Solution: 1st Method:
Average of 1st n natural number is given by = ([n*(n+1)]/2)/n
Average of 1st 97 natural number is given by = {([97*(97+1)]/2)/97} = 49
2nd Method:
These numbers are in AP series, so average,
= (sum of corresponding term)/2
= (1+97)/2 = 49
Or, (2+96)/2 = 49
Or, (3+95)/2 = 49 And so on.
Answer: Option D
Answer: (D) 49
Question: Here 10 programmers, type 10 lines within 10 minutes then 60 lines can type within 60 minutes. How many programmers are needed?
(A) 16
(B) 10
(C) 6
(D) 60
(E) 50
Rationale: 10
10 programmer 10 line 10 mins.
10 programmer 20 line 20 mins.
.
.
.
.10 programmer 60 line 60 mins.
ANSWER:D
Answer: (D) 60
Question: A dog takes 3 leaps for every 8 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 9:8
(B) 9:9
(C) 9:6
(D) 9:1
(E) 9:2
Rationale: Explanation:
Dog : Hare = (3*3) leaps of hare : 8 leaps of hare = 9 : 5.
Answer: A) 9:8
Answer: (A) 9:8
Question: If rupee one produces rupees nine over a period of 54 years, find the rate of simple interest?
(A) 22 1/7 %
(B) 22 3/2 %
(C) 22 1/8 %
(D) 22 1/2 %
(E) 16 2/3 %
Rationale: 9 = (1*54*R)/100
R = 16 2/3 %
Answer:E
Answer: (E) 16 2/3 %
Question: A soft drink company had 5000 small and 12000 big bottles in storage. If 15% of small 18% of big bottles have been sold, then the total bottles remaining in storage is
(A) 14090
(B) 16010
(C) 15060
(D) 14930
(E) 16075
Rationale: 5000 + 12000 - (0.15*5000 + 0.18*12000) = 14090.
Answer: A.
Answer: (A) 14090
Question: A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction ?
(A) 9%
(B) 10%
(C) 7%
(D) 6%
(E) None of these
Rationale: Explanation :
Actual Price = Rs.25 + Rs.2.50 = Rs.27.5
Saving = Rs.2.5
Percentage Saving = (2.5/27.5) × 100 = 250/27.5 = 2500/275
= 100/11 = 9(1/11)% ≈ 9%
Answer : Option A
Answer: (A) 9%
Question: The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?
(A) 776
(B) 240
(C) 872
(D) 2667
(E) 712
Rationale: Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)
Their sum = 10x = 440
x = 44 => 2(x - 2) = 84
Second least number of the other set = 2(84) - 121 = 47
This set has its least number as 46.
Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50
= 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240
Answer: B
Answer: (B) 240
Question: The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 950 gm and 850 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters, what is the weight (in kg) of the mixture?
(A) 3.64
(B) 1.75
(C) 3.52
(D) 2.72
(E) None of these
Rationale: Here's how I did it. My notes from reading the problem were:
1L A = 950 gm
1L B = 850 gm
We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 4L, so 5x = 4 ---> x = 4/5. Each part is 4/5 of a liter.
So if we have 3 parts A, we have 950*3*(4/5) = 2280
If we have 2 parts B, we have 850*2*(4/5) = 1360
2280 + 1360 = 3640
Solving for units gives us 3.64
So the answer is A
Answer: (A) 3.64
Question: Judges will select 4 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
(A) 140
(B) 21
(C) 210
(D) 420
(E) 1,260
Rationale: First Select 4 from 7 contestants and then select top 3 from those 5 =
7C4*4C3 =35 * 4 = 140
ANS:A
Answer: (A) 140
Question: A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of arc ADC when angle D is 155 degrees?
(A) 125
(B) 100
(C) 75
(D) 50
(E) 25
Rationale: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.
An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.
angle D = 155 degrees
Thus,
arc ABC = 310 degrees
A whole circle has 360 degrees of arc, so arc ADC should be the rest of the circle.
arc ADC = 360 - 310 = 50 degrees
Answer =(D)
Answer: (D) 50
Question: what are the number of solutions for x+y+z=12, if x,y & z can take values from 1 to 7 ?
(A) 34
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: if x=1, (y,z) can be (4,7)(5,6)(6,5)(7,4)
if x=2, (y,z) can be (3,7)(4,6)(5,5)(6,4)(7,3)
if x=3, (y,z) can be (2,7)(3,6)(4,5)(5,4)(6,3)(7,2)
if x=4, (y,z) can be (1,7)(2,6)(3,5)(4,4)(5,3)(6,2)(7,1)
if x=5, (y,z) can be (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)
if x=6, (y,z) can be (1,5)(2,4)(3,3)(4,2)(5,1)
if x=7, (y,z) can be (1,4)(2,3)(3,2)(4,1)
Total Combination = 4+5+6+7+6+5+4=37
ANSWER:D
Answer: (D) 37
Question: An error 5% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
(A) 10.4%
(B) 10.25%
(C) 10.23%
(D) 10.26%
(E) 10.5%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (105 x 105) cm2.
(A2 - A1) = [(105)2 - (100)2]
= (105 + 100) x (105 - 100)
= 1025 cm2.
Percentage error = 10.25
B
Answer: (B) 10.25%
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: x pupils in class
total increase = (x*1/2) = x/2
x/2=(83-63) = 20 x= 40
ANSWER D
Answer: (D) 40
Question: Train A and Train B began traveling towards each other from opposite ends of a 500-mile long track at 1:00 PM. If Train A traveled at 25 miles per hour and Train B traveled at 25 miles per hour, at what time did the trains meet?
(A) 5:40 PM
(B) 11:00 PM
(C) 7:20 PM
(D) 8:00 PM
(E) 9:20 PM
Rationale: This question tests your concepts of relative speed:
If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)
If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)
Here the trains are moving towards each other, hence in opposite direction.
Trains will cover the 500 mile track in a time of 500/(25 + 25) = 500/50 = 10 hours
Trains started at 1:00 PM, there they will meet at 11:00 PM
Option B
Answer: (B) 11:00 PM
Question: A bag contains 13 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
(A) 3/16
(B) 4/23
(C) 5/26
(D) 7/34
(E) 9/47
Rationale: Total possible ways to choose three scarves is 13C3 = 286
We need to choose the red scarf and two of 11 other scarves (not the green scarf).
The number of successful possibilities is 11C2 = 55
P(red scarf but not green scarf) = 55/286 = 5/26
The answer is C.
Answer: (C) 5/26
Question: The speed of a boat in still water is 36 kmph. What is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time?
(A) 10 kmph
(B) 14 kmph
(C) 12 kmph
(D) 16 kmph
(E) 15 kmph
Rationale: X = the speed of the stream
(36 + X) / (36 - X) = 2/1
36+ X = 72 - 2X
3X = 36
X = 12 km/hour
If the speed of the stream is 12km/hour, then the 'downstream' speed of the boat is 36+12= 48km/hour and the 'upstream' speed of the boat is 36-12 = 24km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x48 = 96km downstream and 2x24 = 48 km/hour upstream.
Answer : C
Answer: (C) 12 kmph
Question: Find the largest 4 digit number which isexactly divisible by 88?
(A) 2413
(B) 4356
(C) 9944
(D) 7939
(E) 4674
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: (C) 9944
Question: Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?
(A) 4 days
(B) 5 days
(C) 8 days
(D) 9 days
(E) 10 days
Rationale: A and B 1day work = 1/6
B and C 1day work = 1/10
c and A 1day work =1/7.5
A,B,C 1day work =(1/6 + 1/10 + 1/7.5)*1/2=1/5
so A.B.C completes work in 5 days
ANSWER:B
Answer: (B) 5 days