mathewhe/aqua_rat huggingface dataset:
Question: How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
(A) 5
(B) 6
(C) 7
(D) None of these
(E) Cannot be determined
Rationale: Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s
2133 9 (X)
2343 12 (/)
3474 18 (X)
4131 9 (X)
5286 21 (/)
5340 12 (/)
6336 18 (X)
7347 21 (/)
8115 15 (/)
9276 24 (/)
Required number of numbers = 6.
Answer: Option B
Answer: (B) 6
Question: A can do a job in 10 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
(A) 21 ½ days
(B) 22 ½ days
(C) 23 ½ days
(D) 15 days
(E) None of these
Rationale: Explanation:
1/10 + 1/30 = 4/30 = 2/15
15/2 = 15/2 *2 = 15 days
Answer: D
Answer: (D) 15 days
Question: What is the square root of 6,561?
(A) 18
(B) 9
(C) 45
(D) 62
(E) 81
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
81*81=6,561
6561 divided by x = 81
x=81
(E)81
Answer: (E) 81
Question: In a sequence of 12 numbers, each term, except for the first one, is 12^13 less than the previous term. If the greatest term in the sequence is 12^14, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
(A) −12^11
(B) 0
(C) 12^11
(D) 11·12^11
(E) 12^13
Rationale: there are total 12 terms. andgreatestterm is 12^14. Each term is 12^13 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 12^11 less than previous one')
Therefore, 12^14 is the first term of the AP and -12^13 is the difference between successive terms, the smallest term should be the last one.
Last term = First term + (n-1)*d
therefore, Last term = 12^14 + 11*(-12^13)
=> Last term = 12^14 - 11*12^13
=> Last term = 12^13 (12-11) = 12^13
Which is the smallest term.
Hence Ans E it is.
Answer: (E) 12^13
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
(A) 66
(B) 77
(C) 66
(D) 96
(E) 51
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 48 => b + c = 96 --- (2)
From (1) and (2), we cannot find b.
Answer: D
Answer: (D) 96
Question: A bakery currently has 4 pies and 7 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
(A) 1/5
(B) 2/7
(C) 3/7
(D) 1/11
(E) 2/11
Rationale: The total number of ways to choose 5 from 11 is 11C5 = 462.
The number of ways that include 3 pies is 4C3*7C2 = 4*21 = 84
P(exactly 3 pies) = 84/462 = 2/11
The answer is E.
Answer: (E) 2/11
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is
(A) 4 : 5
(B) 5 : 4
(C) 3 : 2
(D) 4 :7
(E) None
Rationale: Let the third number be x.
Then, first number = 120% of x = 120x = 6x
100 5
Second number = 150% of x = 150x = 3x
100 2
Ratio of first two numbers = 6x : 3x = 12x : 15x = 4 : 5.
5 2
A
Answer: (A) 4 : 5
Question: Find the average of all the numbers between 11 and 36 which are divisible by 5.
(A) 25
(B) 77
(C) 20
(D) 28
(E) 10
Rationale: Explanation:
Average = (15 + 20 + 25 + 30 + 35) / 5 = 125/5 = 25
ANSWER: A
Answer: (A) 25
Question: How many positive integers less than 100 have a remainder of 4 when divided by 13?
(A) 6
(B) 7
(C) 4
(D) 9
(E) 10
Rationale: We have to include 4 also.As 13*0 + 4 =2
If somebody says to divide 4 by 13 ,we will be telling we have 0 quotient and remainder as 4.
Answer is C
Answer: (C) 4
Question: Robin is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of COKE. The pattern repeats after she leaves the morsel of rye. If Robin drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
(A) rye − wheat − wheat
(B) wheat − wheat − white
(C) white − rye − wheat
(D) white − white − white
(E) COKE- WHEAT-WHEAT
Rationale: Q is nothing BUT asking about remainder..
total morsels thrown before the pattern is repeated = 2+3+1 = 6..
so REMAINDER when 2000 is div by 6..
1998 is EVEN and also div by 3, so remainder is 2..
Last 3 of morsels are 1998-1999-2000
so he uses the last of morsel of pattern in 1998 two of the first morsels of the pattern in 1999 and 2000, and the pattern is w, w, W, W, W, C..
ans C-w-w
E
Answer: (E) COKE- WHEAT-WHEAT
Question: If x and y are integers and |x - y| = 10, what is the minimum possible value of xy?
(A) -9
(B) -18
(C) -24
(D) -25
(E) -48
Rationale: Sometimes the answer choices to a given question provide a big 'hint' as to how you can go about solving it. This prompt can also be solved without any complex math ideas - you just need to do a bit of 'brute force' math and you'll have the answer relatively quickly.
We're told that X and Y are INTEGERS and |X - Y| = 10. We're asked for the MINIMUM possible value of (X)(Y).
Since all of the answer choices are NEGATIVE, this tells us that ONE of the two variables MUST be negative (and the other must be positive), so we should restrict our work to those options.
IF...
X = 9, Y = -1, then XY = -9
X = 8, Y = -2, then XY = -16
X = 7, Y = -3, then XY = -21
X = 6, Y = -4, then XY = -24
X = 5, Y = -5, then XY = -25
X = 4, Y = -6, then XY = -24
X = 3, Y = -7, then XY = -21
From this, we can conclude the XY will start to get bigger as X continues to decrease down to 1, so there's no need to do any additional work.
Final Answer:
D
Answer: (D) -25
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) Rs.6620
(B) Rs.1258
(C) Rs.3556
(D) Rs.974
(E) Rs.456
Rationale: A = 20000(11/10)3
= 26620
26620-20000=Rs.6620
Answer:A
Answer: (A) Rs.6620
Question: In triangle XYZ, side XY, which runs perpendicular to side YZ, measures 24 inches in length. If the longest side of the the triangle is 26 inches, what is the area, in square inches, of triangle XYZ?
(A)  100
(B)  120
(C)  140
(D)  150
(E)  165
Rationale: Okay we know we have a right triangle with hypotenuse 26.
Using Pythagoras theory I think: 24^2 + x^2 = 26^2
so 576 + x^2 = 676 ---> x^2 = 100 ---> x= 10
Areal of triangle = base* height / 2 so 24*10/2 = 120
So answer choice B
Answer: (B)  120
Question: The length of minute hand of a clock is 5.5 cm. What is the area covered by this in 10 minutes
(A) 15.27
(B) 16.27
(C) 17.27
(D) 19.27
(E) 15.83
Rationale: area of circle is pi*r^2
but in 10 minutes area covered is (10/60)*360=60 degree
so formula is pi*r^2*(angle/360)=3.14*(5.5^2)*(60/360)=15.83 cm^2
ANSWER:E
Answer: (E) 15.83
Question: After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 700 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ?
(A) 2160
(B) 2350
(C) 2000
(D) 2300
(E) 1800
Rationale: Explanation :
Total Exp = 5000+1500+4500+2500+2000+700 = 16200
Exp in % = 100-10 = 90%, 16200 = 90%
Saving = 10 % = 16200 X 10/90 = Rs. 1800
Answer : E
Answer: (E) 1800
Question: What is the least number which when divided by 6, 9, 12 and 18 leaves remainder 4 in each care?
(A) 30
(B) 40
(C) 36
(D) 56
(E) 66
Rationale: Explanation:
LCM of 6, 9, 12 and 18 is 36
Required number = 36 + 4 = 40
Answer: Option B
Answer: (B) 40
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 7 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 50
Rationale: Ans.(D)
Sol. Number of choices to go by ship = 7 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 7 x 5 = 35 ways
Answer: (D) 35
Question: In a batch of 125 students, there are 12 books related with different subjects to be distributed. If the total number of books bought during the time of distribution were 1511, how many extra books will be lying with the distributor?
(A) 10
(B) 11
(C) 2
(D) 5
(E) 3
Rationale: 125x12=1500 is the total number of books required to be distributed. As the number of books actually bought during the time of distribution 1511, 11 extra books were purchased. Answer: B
Answer: (B) 11
Question: A company pays project contractors a rate of a dollars for the first hour and b dollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 4 and 6 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
(A) Per month, with savings of $(3a + 3b)
(B) Per month, with savings of $(3a - 3b)
(C) The two options would cost an equal amount.
(D) Per project, with savings of $(3a + 3b)
(E) Per project, with savings of $(3a - 3b)
Rationale: Per Project, company will pay as follows:
For 4 hours work = a+3b
For 6 hours work = a+5b
Total = 2a+8b
Per Month, company will pay for 10 hours work = a+9b
Total per contract - total per month
4a+6b - (a+9b)
3a-3b
Since a>b Amount 4a+6b(per contract amount) > a+9b (per project amount) by 3a-3b.
Hence per month payment will be cheaper by 3a-3b .
OA B
Answer: (B) Per month, with savings of $(3a - 3b)
Question: In Prasanna's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Prasanna and he thinks that Prasanna's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Prasanna?
(A) 67 kg
(B) 68 kg
(C) 66.5 kg
(D) 69 kg
(E) NOne
Rationale: Sol.
Let Prasanna's weight be X kg.
According to Prasanna, 65 < X < 72.
According to Prasanna's brother, 60 < X < 70.
According to Prasanna's mother, X < 68.
The value satisfying all the above conditions are 66 and 67.
∴ Required average = [ 66 + 67 / 2 ] = [133 / 2] = 66.5 kg.
Answer C
Answer: (C) 66.5 kg
Question: In a mixture of 45 litres, the ratio of acid to base is 4 : 1. How much base must be added to make the mixture ratio 3 :2?
(A) 72 lts
(B) 24 lts
(C) 15 lts
(D) 1.5 lts
(E) 2.5 lts
Rationale: Base = 9 litres
Acid = 9 lts
To make the ratio of acid : base as
3 : 2,
15 litres of base must be added.
ANSWER:C
Answer: (C) 15 lts
Question: (7895632 x 881) = ?
(A) 6846381250
(B) 6584638130
(C) 6584638135
(D) 6584638140
(E) 6956051792
Rationale: 7895632 x 881=6956051792Ans E
Answer: (E) 6956051792
Question: A plot is sold for Rs. 18,700 with a loss of 15%. At what price it should be sold to get profit of 15%.
(A) Rs 25300
(B) Rs 22300
(C) Rs 24300
(D) Rs 21300
(E) None of above
Rationale: Explanation:
This type of question can be easily and quickly solved as following:
Let at Rs x it can earn 15% pr0fit
85:18700 = 115:x [as, loss = 100 -15, Profit = 100 +15]
x = (18700*115)/85
= Rs.25300
Option A
Answer: (A) Rs 25300
Question: Six friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?
(A) 11%
(B) 14%
(C) 20%
(D) 22%
(E) 26%
Rationale: Let x be the original price of one ticket.
The total original cost is 6x.
The new cost is 7y, where y is the discounted price of one ticket.
6x = 7y
y = 6x/7 which is about 0.86x which is a discount of about 14%.
The answer is B.
Answer: (B) 14%
Question: Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 12 min
(B) 15 min
(C) 25 min
(D) 50 min
(E) 20 min
Rationale: Part filled by A in 1 min. = 1/20
Part filled by B in 1 min. = 1/30
part filled by (A + B) in 1 min. = 1/20 + 1/30 = 1/12.
Both the pipes can fill the tank in 12 minutes.
ANSWER:A
Answer: (A) 12 min
Question: A retailer bought a hat at wholesale and marked it up 60% to its initial price of $24. By how many more dollars does he need to increase the price to achieve a 100% markup?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let x be the wholesale price.
Then 1.6x= 24 and x = 24/1.6 = 15.
To achieve a 100% markup, the price needs to be $30.
The retailer needs to increase the price by $6 more.
The answer is D.
Answer: (D) 6
Question: Compare the rates of two trains, one travelling at 45 km/hr and other is at 10m/s?
(A) 5:4
(B) 3:2
(C) 1:5
(D) 2:7
(E) 3:5
Rationale: speed of the 1st train = 45km/hr
speed of the 2nd train = 10m/s = 10*18/5 = 36km/hr
ratio of the speeds of the train = 45:36 = 5:4
Answer is A
Answer: (A) 5:4
Question: If P, x, y, and z are positive integers and (x)×(y)×(z)=P^2, which of the following could be the values of x, y, and z?
(A) 3, 16, 25
(B) 9, 25, 24
(C) 2, 49, 32
(D) 2, 9, 16
(E) 8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*49*32 = 2*7*7*8*4 = 7*7*8*8
Ans C
Answer: (C) 2, 49, 32
Question: A train is running between Patna to Howrah.Seven people enter the train somewhere between Patna and Howrah.It is given that nine stops are there between patna and howrah.In how many ways can the tickets be purchased if no restriction is there with respect to the number of tickets at any station?(2 people donot buy the same ticket)
(A) 45c7 ways
(B) 45c6 ways
(C) 44c7 ways
(D) 46c7 ways
(E) 45c8 ways
Rationale: P _ _ _ _ _ _ _ _ _ H
P 1 2 3 4 5 6 7 8 9 H
If those people enter in the 1st station, the no. of ways they can buy tickets: 9 ways
If those people enter in the 2nd station, the no. of ways they can buy tickets: 8 ways
.
.
If those people enter in the 9th station, the no. of ways they can buy tickets: 1 way
Now total no. of ways to buy tickets are: 9+8+7+6+5+4+3+2+1=45
So, the tickets can be purchased by 7 people is 45c7 ways
ANSWER:A
Answer: (A) 45c7 ways
Question: How many positive integers between 5 and 5000(both are inclusive) are there such that they are multiples of 5?
(A) 1500
(B) 1000
(C) 999
(D) 1001
(E) 1005
Rationale: Multiples of 5 = 5,10,15-----,5000
Number of multiples of 5 => 5000-5/5+1= 1000
Answer is B
Answer: (B) 1000
Question: If x^2 - 9 = 0 and x > 0, which of the following must be equal to 0 ?
(A)  x^2 - 9x
(B)  x^2 - 9x + 20
(C)  x^2 - 2x + 3
(D)  x^2 + 2x - 3
(E)  x^2 - 5x + 6
Rationale: x^2-9 = 0
x= +3 or x = -3
if we substitute x= 3 in the equation x^2 -5x+6 = 9-15+6 = 0
E is also the answer
Answer: (E)  x^2 - 5x + 6
Question: Fifty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
(A)  60
(B)  80
(C)  84
(D)  120
(E)  140
Rationale: 50% of the members have passed the test, thus 50% have not passed the test.
We also know that 30+12=42 members have not passed the test, thus 0.5*Total=42 --> Total=84.
Answer: C.
Answer: (C)  84
Question: f n = 3^2 - 2^2, which of the following is NOT a factor of n?
(A) 5
(B) 10
(C) 4
(D) 15
(E) 20
Rationale: 9-4 =5 is prime no. any number not multiply with five is not a factor
C
Answer: (C) 4
Question: If 125% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 20% of m is equal to what percent of 150% of j ?
(A) 0.35
(B) 466
(C) 35
(D) 350
(E) 3500
Rationale: IMO answer should be 350...
consider j=10, then k=50, l=150 and m=350....
20% of 350, comes out to be 70....
150% of 10 is 15....
(70*100)/15=466.66....
Ans : B
Answer: (B) 466
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 32 km
(B) 25 km
(C) 28 km
(D) 24 km
(E) None of these
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
ANSWER:E
Answer: (E) None of these
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
(A) Rs. 8,400 .
(B) Rs.10,000
(C) Rs. 11,980
(D) Rs. 13,600
(E) Rs.14,700
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. 35000x (21/50)= Rs. 14,700.
answer :E
Answer: (E) Rs.14,700
Question: Which of the following equations has a root in common with x^2−4x+3=0 ?
(A) x^2-4x-4=0
(B) x^2-2x+1=0
(C) x^2-x-1=0
(D) x^2-10x-1=0
(E) x^2+1=0
Rationale: If we carefully look at the given equation we can arrange it in the following manner:
(x-1)(x-3) = 0
so the two roots are 1 and 3.
Now put 1 and 3 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 1: we get -7; Putting 3 we get -7. Reject this option.
(B) putting 1: we get 0. This is the equation.
We are lucky. No need to check other options.
B is the answer.
Answer: (B) x^2-2x+1=0
Question: 2 cyclist begin training at same time A complete each lap in 4 sec B in 6 minutes how many minutes after start will both cyclist pass at exactly same spot when they begin to cycle
(A) 160 seconds
(B) 260 seconds
(C) 360 seconds
(D) 460 seconds
(E) 560 seconds
Rationale: 6 minutes= 360 sec
lcm of 4, 360 is 360
so they meet after 360 seconds
ANSWER:C
Answer: (C) 360 seconds
Question: The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 208, how many such sequences can be formed?
(A) 26
(B) 17
(C) 25
(D) 33
(E) 50
Rationale: Four consecutive odd numbers: k-2, k, k+2, k+4
Three consecutive even numbers: n-2, n, n+2
k-2+k+k+2+k+4=n-2+n+n+2
4k+4=3n
4(k+1)=3n
k+1=(3/4)n
k=(3/4)n-1
All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range:
We know,
101<n<208
104<=n<=204
Count=(204-104)/4+1=100/4+1=25+1=26
Ans: 26.
Answer: (A) 26
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,74,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
(A) 0.20833
(B) 0.14544
(C) 0.25632
(D) 0.2139
(E) 0.63435
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 374000x
\therefore Required percentage = \inline \frac{800x}{374000}\times 100 = 0.21390
D
Answer: (D) 0.2139
Question: A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?
(A) 20
(B) 30
(C) 48
(D) 60
(E) 72
Rationale: Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 16
Time traveled in bike = t2
d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 16*t2 = 80
t1 + 2*t2 = 10 ----- (1)
Given: t1 + t2 = 8 ----- (2)
(1) - (2) --> t2 = 2 and t1 = 8 - 2 = 6
Walking distance = s1*t1 = 8*6 = 48
Answer: C
Answer: (C) 48
Question: Calculate 24 x 99
(A) 2976
(B) 2467
(C) 2476
(D) 4276
(E) 2376
Rationale: = 24-1 = 23
= (Decrement each digit of the number obtained from 9) Here we got 23. Now
= 9-2 = 7 and 9-3=6. So we have 76
Just write these numbers together.
That is we have 23 and 76.
Hence answer is 2376
Answer is E.
Answer: (E) 2376
Question: Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 4 more than the average expenditure of all the nine. The total money spent by all of them was
(A) 31.5
(B) 40
(C) 29.25
(D) 27
(E) None of the above
Rationale: Let the average expenditure of all the ninte be x
Then, 3 × 8 + x + 4 = 9x
⇒ x = 3.5
∴ Total money spent = 9x = 9 × 3.5 = 31.5
Answer A
Answer: (A) 31.5
Question: Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $6,500, what is the bonds face value?
(A)  $5,200
(B)  $6,750
(C)  $7,425
(D)  $7,500
(E)  $9,375
Rationale: Interest = 0.05*face value = 0.04*6,500 --> face value = 0.04*6,500/0.05 = 5,200.
Answer: A.
Answer: (A)  $5,200
Question: Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?
(A) 2000
(B) 3000
(C) 4000
(D) 1000
(E) 5000
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
Answer:B
Answer: (B) 3000
Question: A vendor sells 80 percent of the pears he had and throws away 50 percent of the remainder. The next day, the vendor sells 80 percent of the remaining pears and throws away the rest. In total, what percent of his pears does the vendor throw away?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Let x be the original number of pears.
On day one, the vendor throws away (0.5)(0.2)x=0.1x.
The remaining pears are (0.5)(0.2)x = 0.1x.
On day two, the vendor throws away (0.2)(0.1)x=0.02x.
The vendor throws away a total of 0.1x + 0.02x = 0.12x.
The vendor throws away 12 percent of the pears.
The answer is D.
Answer: (D) 12
Question: If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+89)=?
(A) 6150
(B) 6200
(C) 6050
(D) 6075
(E) 5075
Rationale: Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 89=1+(n-1)2
=> n=45
Use value of n in (1)
then,
Sn = (45/2)(1+89) = 2025
Ans:- 3(Sn) = 6075
Answer : D
Answer: (D) 6075
Question: Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?
(A) $22
(B) $24
(C) $30
(D) $36
(E) $40
Rationale: B its is.
Let price = X
(x-1)8 = 6X
X= 4
hence total money = 6*4= 24
Answer: (B) $24
Question: A survey was sent to 90 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
(A) 2%
(B) 6%
(C) 14%
(D) 28%
(E) 63%
Rationale: case 1: (7/90)=x/100
x=8%
case 2: (9/63)=y/100
y=14%
So percent increase is =(y-x)=(14-8)%=6%
Answer is B
Answer: (B) 6%
Question: Population of a city in 20004 was 1500000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 354354
(B) 545454
(C) 465785
(D) 456573
(E) 3251625/2
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 3251625/2
E
Answer: (E) 3251625/2