MU-NLPC/Calc-aqua_rat huggingface dataset:
10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range T of the 10 numbers?	Choose the most appropriate option:  A) 25  B) 27  C) 30  D) 52  E) 55

Solution: Positions: 1 2 3 4 5 6 7 8 9 10   Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b   y - x = 25   Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.   b - a = 30 --> b = 30 + a   In order to increase the range, we have to maximize the value of 'b'.   'b' can be maximized by taking the max value of 'a'.   From the assumed values, maximum value of 'a' can be 22.   Therefore, b = 30 + 22= 
30 + 22 = 52
52   Range T= 52 - 0= 
52 - 0 = 52
52   Answer: 52
Answer: D
The operation is defined for all integers a and b by the equation ab = (a - 1)(b - 1). If y12 = 110, what is the value of y ?  Choose the correct choice from the following answers:
A) 11	B) 12	C) 13	D) 15	E) 18

Solution: ab = (a - 1)(b - 1)   y12 = (y-1)(12-1) =110 --> y-1=10 --> y=11   11nswer: 11
Answer: A
In an office one half of the employees are in account section,quarter are in printing section,one-fifth are stock section and the other 50 are supervisors. How many employees total are there in the office?  Choose the correct choice from the following:
A) 250  B) 366  C) 400  D) 500  E) 1000

Solution: 1/2x + 1/4x +1/5x = 19/20x   Remaining 1/20 x= 50   x= 50*20= 
50*20 = 1_000
1000   1000 is the answer.
Answer: E
A swimming pool can be filled by pipe A in 3 hours and by pipe B in 6 hours, each pump working on its own. At 9 am pump A is started. At what time will the swimming pool be filled if pump B is started at 10 am? Choose the correct choice from the following answers
A) 11:20
B) 11:30
C) 11:40
D) 11:50
E) 11:60

Solution: the rates of the two pumps are   pump A: 1 / 3 , pump B: 1 / 6   Working together, If pump A works for t hours then pump B works t - 1 hours since it started 1 hour late. Hence   t * (1 / 3) + (t - 1) * (1 / 6) = 1   Solve for t   t = 7 / 3 hours = 2.3 hours = 2 hours 20 minutes.   The swimming pool will be filled at   9 + 2:20 = 11:20   11:20nswer 11:20
Answer: A
If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails, on the second toss the coin lands on heads, and then lands on tails on the last toss?  Choose the correct choice from the following options.
A) 1/8  B) 1/3  C) 1/4  D) 1/2  E) 1

Solution: P(THT) = 1/2*1/2*1/2=1/8   The answer is 1/8.
Answer: A
Jaya ranks 5th in a class of 53. What is her rank from the bottom in the class? Choose the correct option
A) 49th
B) 48th
C) 47th
D) 50th
E) None of these

Solution: There are 4 students above her.   When takan from bottom there are 4 students below her rank .   So her rank wud be 53-4 i.e. 49th.   49thNSWER:49th
Answer: A
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?	Choose the most appropriate option.
A) 49%	B) 30%	C) 40%	D) 44%	E) 41%

Solution: The total CP = Rs. 16000 + Rs. 6250   = Rs. 22250 and SP   = Rs. 31150   Profit(%) = (31150 - 22250)/22250 * 100= 
(31150 - 22250)/22250 * 100 = 40
40%   Answer: 40%
Answer: C
A train of 45 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?  Choose one:
A) 6 B) 3 C) 4.2 D) 9 E) 4

Solution: D = 45 * 60 + 1500= 
45 * 60 + 1500 = 4_200
4200 m   T= 4200/60 * 18/5= 
4200/60 * 18/5 = 252
252 sec= 4.2 mins   Answer:4.2
Answer: C
Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 42, find the ages of Toby and Debby?	Choose the correct choice from the following choices: A) 6 and 14 B) 5 and 9 C) 8 and 10 D) 5 and 10 E) 8 and 16

Solution: Let the age of Debby be x and Toby be x-4   3 ( x + x-4 ) = 42   x = 9   The ages of Toby and Debby are 5 and 9.   Answer : 5 and 9
Answer: B
what is the cost price of an article sold at rs.199 after two successive discount of 10% and 15%? Choose the correct option: A) 220 B) 230 C) 240 D) 250 E) 260

Solution: cost price=199*100/90*100/85   =260   ANSW260R:260
Answer: E
In what ratio should a variety of Rice costing Rs. 10 per kg be mixed with another variety of Rice costing Rs. 13.25 per kg to obtain a mixture costing Rs. 10.75 per kg?
Choose the correct answer
A) 2 :1 B) 1 :2 C) 5 :1 D) 4 :1 E) 3:1

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   By the rule of allegation, x/y = (13.25 - 10.75) / (10.75 - 10) = 6/3= 
6/3 = 2
2/1   2 :1NSWER:2 :1
Answer: A
How many different ways can you select a pilot and a co pilot if you have 30 people to choose from?
Choose the most appropriate option:
A) 870  B) 920  C) 1398  D) 4950  E) 9900

Solution: You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.   So the answer is in a sense (30C2) x 2 = 870.   870ns 870
Answer: A
If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?  Select the correct option
A) 100 m  B) 200 m  C) 300 m  D) 400 m  E) 500 m

Solution: perimeter of rectangle=2(l+b)   2(l + 100) = 600   => l = 200 m   ANSWER:200 m
Answer: B
The distance from Steve's house to work is 40 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
Choose the correct choice
A) 5.
B) 10.
C) 14.
D) 15.
E) 20.

Solution: Time is in the ratio 2:1 :: to: fro office   Therefore, 2x+1x=6 hrs   Time take to come back - 2 hrs, distance travelled - 40km => Speed = 20kmph   20.
Answer: E
Find the simple interest on $2000 for 3 years at 10% per annum?
Choose the most appropriate option
A) $250  B) $300  C) $500  D) $600  E) $1000

Solution: SI = PTR/100   = 2000*3*10/100= 
2000*3*10/100 = 600
$600   Answer is $600
Answer: D
If n is the product of the integers from 1 to 11, inclusive, how many different prime factors greater than 1 does n have? Choose one:
A) Four
B) Five
C) Six
D) Seven
E) Eight

Solution: n = 1*2*3*4*5*6*7*8*9*10*11   The prime factors of n are 2, 3, 5, 7, and 11.   There are 5 prime factors.   The answer is Five.
Answer: B
A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability W that you can still row the canoe?	Pick one:
A) 9/25  B) 10/25  C) 6/10  D) 2/3  E) 21/25

Solution: Simply look at the question from the other side. What is the probability that you can’t row the canoe? This would be 2/5 x 2/5 = 4/25.   Using the idea that the probability of something happening is 1 – the probability that it doesn’t happen, you can use the following equation to reach the right answer W: 1 – 4/25 = 21/25.Answer choice 21/25.
Answer: E
A train covers a certain distance at a speed of 250kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of  Choices: A) 400km/hr B) 500km/hr C) 600km/hr D) 700km/hr E) 800km/hr

Solution: Explanation:   Distance = 250×4 = 1000km   Required speed = (1000/2)= 
(1000/2) = 500
500km/hr   Answer: Option 500km/hr
Answer: B
Which of the following is a prime number
Choose the correct answer
A) 9  B) 2  C) 4  D) 8  E) 9

Solution: Explanation:   A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself.   So from above options 2 is that number   Answer: Option 2
Answer: B
A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:2:2, respectively, but he wanted to make more money, so he shifted the ratio to 2:2:5, respectively. How many more acres of land were planted with tobacco under the new system? Choose one: A) 90 B) 150 C) 270 D) 300 E) 450

Solution: Originally (2/9)*1350= 
(2/9)*1350 = 300
300 acres were planted with tobacco.   In the new system (5/9)*1350= 
(5/9)*1350 = 750
750 acres were planted with tobacco.   Thus   750-300= 
  750-300 = 450
450 more acres were planted with tobacco.   The answer is 450.
Answer: E
At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 40 other employees of Company K, how many employees does Company K have?	Select the correct option:
A) 160  B) 180  C) 190  D) 200  E) 400

Solution: Let the total number of employees in the company be x   % of secretaries = 15%   % of salespeople = 60%   % of of employees other than secretaries and salespeople = 100 - 75= 
100 - 75 = 25
25%   But this number is given as 40   so 25% of x= 40   x = 160   Therefore there a total of 160 employees in the company K   Correct answer - 160
Answer: A
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?	Choose the correct choice from the following answers:  A) 27  B) 28  C) 200  D) 277  E) 267

Solution: d2/2 = (20 * 20)/2= 
(20 * 20)/2 = 200
200   Answer:200
Answer: C
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?  Choices:
A) 17 1/6
B) 17 1/3
C) 17 1/7
D) 17 1/2
E) 17 1/1

Solution: 1/20 + 1/30 - 1/40   = 7/120   120/7   = 17 1/7   Answer: 17 1/7
Answer: C
10 books are placed at random in a shelf. The probability that a pair of books will always be together is ? Choose the correct choice from the following.
A) 1/7
B) 2/5
C) 1/5
D) 1/3
E) 3/5

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability   = 1/5   Answer:1/5
Answer: C
The average salary of all the workers in a workshop is Rs. 10000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 8000. The total number of workers in the workshop is :  Choose the correct option:  A) 14  B) 21  C) 88  D) 37  E) 29

Solution: Explanation:   Lot the total number of workers be v Then,   10000v = (12000 * 7) + 8000 (v - 7) <=> 2000v = 28000 <=> v = 14   14nswer: 14) 14
Answer: A
Pipe A and pipe B fill water into a tank of capacity 1000 litres, at a rate of 200 l/min and 50 l/min. Pipe C drains at a rate of 25 l/min. Pipe A is open for 1 min and closed, then pipe B is open for 2 min and closed. Further the pipe c is opened and drained for another 2 min. This process is repeated until the tank is filled. How long will it take to fill the tank?  Choose the correct choice from the following
A) 15 B) 17 C) 18 D) 56 E) 20

Solution: tank capacity: 1000 L,   1st- 200 l/min for 1 min, volume filled: 200 L   2nd- 100 l/min for 2 min, volume filled: 100 L   3rd (water draining) : 25 l/min*2 : 50 L   total :  (200+100)-50= 
 (200+100)-50 = 250
250 L filled for 1 cycle   number of 250 in 1000 L tank :1000/250= 
1000/250 = 4
4   time taken to fill: 4* total time= 4*5= 
4*5 = 20
20 (option 20)
Answer: E
The sum of money at compound interest amounts to thrice itself in 5 years. In how many years will it be 21 times itself?  Choose the correct choice:
A) 18 years  B) 9 years  C) 12 years  D) 16 years  E) 30 years

Solution: 100 ---- 300 --- 5   900 --- 5   1200---5   1500----5   1800---5   2100---5   6 years   Answer: 30 years
Answer: E
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
Select the correct option
A) 13	B) 25	C) 17	D) 12	E) 11

Solution: 11 cartons total   7 large boxes (7 * 8 = 56 boxes)   4 small boxes (4 *10 = 40 boxes   11 total cartons and 96 boxes
Answer: E
What is the least possible product of 4 different integers, each of which has a value between –2 and 10, inclusive?
Pick one:
A) –5040  B) –3600  C) –720  D) –1440  E) –120

Solution: Maximize the total product with a -ve sign   so -2 * 10 * 9 * 8 = 720 * -2 = -1440   Answer is –1440.
Answer: D
How many odd prime numbers are there less than 75? Choose the correct choice from the following options
A) 20	B) 1	C) 2	D) 16	E) 17

Solution: Odd prime number less than 75:3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73   There is 20 the odd prime number   20nswer is 20
Answer: A
Suresh invested a sum of Rs. 15000 at 9 percent per annum Simple interest and Rs. 12000 at 8 percent per annum compound interest for a period of 2 years. What amount of interest did Suresh earn in 2 years?
Options
A) 4496.8	B) 4596.8	C) 4696.8	D) 4796.8	E) 4896.8

Solution: S.I = PTR/100   S.I =15000*9*2/100   S.I= 2700   4696.8.I =P(1+r/100)^n -P   4696.8.I= 12000(1+8/100)^2-12000   4696.8.I=1996.8   total amount in 2 years   as interest = S.I +4696.8.I   = 2700+1996.8= 
2700+1996.8 = 4_696.8
4696.8   ANSWER:4696.8
Answer: C
Anish borrowed 15000 at the rate of 12% and an other amount at the rate of 15% for two years. The total interest paid by him was 9000. How much did he borrow? Answers
A) 32,000	B) 33,000	C) 30,000	D) 35,000	E) None of these

Solution: Let x be the other amount   \ 3x⁄10 + 3600 = 900 ⇒ x = 18000   \ total borrowed sum = 33000   Answer 33,000
Answer: B
Let A represent a set of four distinct prime numbers. If the sum of the numbers in A is even and x is a member of A, then what is the least possible value that x can be?	Pick one
A) 1  B) 2  C) 3  D) 5  E) 7

Solution: We are told that A is a set of four distinct prime numbers, and the sum of the numbers in A is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.   If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of A must be odd to yield an even sum.   Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.   The correct answer is choice (C).   Note:1 is not a prime number.
Answer: C
An eight-digit telephone number consists of exactly two zeroes. One of the digits is repeated thrice. Remaining three digits are all distinct. If the first three digits (from left to right) are 987, then find the probability of having only one 9, one 8 and one 7 in the telephone number.	Choose one:
A) 1/18  B) 1/20  C) 1/10  D) 5/47  E) 5/45

Solution: Explanation :   Case A: There is only one 9, one 8 and one 7 in the number.   Hence there has to be one digit from {1,2,3,4,5,6} repeated thrice.   Total number of ways in which such a number can exist is :   =>6C1×5!/(3!×2!).   =60.   Case B: One of the three digit {9,8,7} is repeated thrice.   Hence, there will be one digit from {1,2,3,4,5,6}.   Total number of ways in which such a number can exist:   =>3C1×6C1×5!/(3!×2!).   =>540   Total possible telephone numbers:   =60+540= 
60+540 = 600
600.   Hence the required Probability is 60/600= 1/10.   Answer : 1/10
Answer: C
A room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
Choose the correct answer.
A) 10
B) 15
C) 17
D) 19
E) 21

Solution: Let us calculate both the length and width of the room in centimeters.   Length = 7 meters and 20 centimeters = 720 cm   width = 4 meters and 32 centimeters = 432 cm   As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.   Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 720 and 432 = 144   Thus, the number of square tiles required = (720 x 432 ) / (144 x 144) = 5 x 3 = 15   Answer: 15
Answer: B
The ratio of Rita's age to her mother's age is 3:8. The difference of their ages is 35 years. The ratio of their ages after 4 years will be: Choose the correct choice from the following choices:
A) 7:12 B) 5:12 C) 38:43 D) 42:47 E) 52:47

Solution: Rita age=3x   mother's age=8x   their difference = 8x-3x=35   x=7   therefore Rita's current age=21   mother's current age=56   4 years hence their ratio of ages will be 25:60   ans is 5:12   ANSWER:5:12
Answer: B
City A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip? Choose the most appropriate option.
A) 57	B) 57.5	C) 58.2	D) 59	E) 62

Solution: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,   Average Speed=(Total DistanceTotal Time)=2304=57.5   57.5
Answer: B
In how many W ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
Choose the correct choice from the following options:	A) 6	B) 12	C) 18	D) 24	E) 30

Solution: Number of ways of arranging the word GMAT = 4! = 24   Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6   Number of ways of arranging GMAT so that A is not in the beginning W= 24 - 6= 
24 - 6 = 18
18   Answer: 18
Answer: C
What is the least integer greater than –1+0.5? Select.
A) –2	B) –1	C) 0	D) 1	E) 2

Solution: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.   First, let's take care of the Arithmetic:   (-1) + (0.5) = -0.5   On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -1 to -0.5).   Next, the question asks for the LEAST integer that is GREATER than -0.5   Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -0.5 is 0.   Final Answer:   0
Answer: C
A watch was sold at a loss of 8%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price? Choose the correct option
A) 1000 B) 2876 C) 1977 D) 1167 E) 2711

Solution: 92%   104%   --------   12% ---- 140   100% ---- ? => Rs.1167   Answer: 1167
Answer: D
25 x 10 + 25 x 11 = ?  Choices: A) 725 B) 720 C) 600 D) 525 E) None of them

Solution: =25 x (10+11) (by distributive law)   =25 x 21   =525   Answer is 525
Answer: D
A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
Pick:
A) 288
B) 277
C) 299
D) 500
E) 278

Solution: P - 340 = (P*4*8)/100   P = 500   Answer:500
Answer: D
If x-y=8, which of the following must be true?
I. If x is positive, y must be positive
II. If x is negative, y must be negative
III.Both x and y are positive
Select the correct option
A) I only	B) II only	C) III only	D) I and II	E) II and III

Solution: If x-y=8, which of the following must be true?   I. Both x and y are positive   II. If x is positive, y must be positive   III. If x is negative, y must be negative   1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D   2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate II only and E   A) I only   II only) II only   C) III only   D) I and II   E) II and III   Answer II only
Answer: B
The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 18 kmph, 17 kmph, and 16 kmph respectively. What is the ratio of the time taken by B to than taken by D?
Answers:
A) 5:16	B) 5:17	C) 9:8	D) 8:9	E) None of these

Solution: Explanation :   Since it is a relay race, all the runners ran the same distance.   Hence for a same distance, (ratio of times) = 1/(ratio of speeds).   Hence ratio of times taken by B t& D = 16 : 18 = 8 : 9.   Answer : 8:9
Answer: D
If 5x = 6y and xy ≠ 0, what is the ratio of 1/5*x to 1/8*y ?
Answers:
A) 48/25	B) 36/25	C) 6/5	D) 5/6	E) 25/36

Solution: 5x = 6y => x/y = 6/5   1/5*x to 1/8*y = x/y * 8/5 = (6/5)*(8/5)=48/25   48/25ns: 48/25
Answer: A
What is the next number of the following sequence
3,7,13,21,?  Choose the correct choice:	A) 22	B) 31	C) 41	D) 35	E) 42

Solution: 2^2-1=3   3^2-2=7   4^2-3=13   5^2-4=21   6^2-5=31   ANSWER:31
Answer: B
A discount electronics store normally sells all merchandise at a discount of 10 percent to 40 percent off the suggested retail price. If, during a special sale, an additional 5 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $500 before any discount?
Options:
A) $130.00
B) $285.00
C) $200.00
D) $258.00
E) $210.00

Solution: Original price : 500 $   Max first discount = -40%   Thus : 500âˆ—(1âˆ’40/100)=300   Second discount on the discounted price = -20%   Thus : 300âˆ—(1âˆ’5/100)=285   Answer $285.00.
Answer: B
Find the total average marks of all the students in 2 separate classes, if the average marks of students in the first class of 39 students is 45 and that of another class of 35 students is 70.
Choose the correct choice from the following:
A) 55.8  B) 51.8  C) 53.8  D) 56.8  E) 52.8

Solution: Sum of the marks for the class of 39 students = 39 * 45= 
39 * 45 = 1_755
1755   Sum of the marks for the class of 35 students= 35 * 70= 
35 * 70 = 2_450
2450   Sum of the marks for the class of 74 students=1755+2450= 
1755+2450 = 4_205
4205   Average marks of all the students= 4205/74   = 56.8   Answer:56.8
Answer: D
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?	Choose the correct option:	A) 87 kmph	B) 68 kmph	C) 14 kmph	D) 76 kmph	E) 57 kmph

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream   = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 42/3= 
42/3 = 14
14 kmph.   Answer:14 kmph
Answer: C
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 29. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?  Choose the correct choice from the following options.
A) 1  B) 13  C) 15  D) 21  E) 47

Solution: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.   What does this imply?If the sum of the first n terms of the sequence is n   Since number of terms will definitely be positive, we are looking for a positive sum.   19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on   Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...   Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.   Answer (21)
Answer: D
In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $847,000 invested in preferred stocks, what is the total amount of money invested in the fund? Choose the correct answer.
A) $1,974,000  B) $2,538,000  C) $3,264,000  D) $3,826,000  E) $4,235,000

Solution: Portion invested in preferred stock = 3/5 * 1/3 = 1/5   1/5 of fund = 847---   Fund = 5 * 847---   Here, we can avoid the math and simply look at 5 * 7 -> 35. Only option E has 35 in it.   Answer ($4,235,000).
Answer: E