MU-NLPC/Calc-aqua_rat huggingface dataset:
In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-9, 1), (1, 1), (1, -8) and (-9, -8)?
Choose the most appropriate option:
A) 72	B) 180	C) 70	D) 90	E) 140

Solution: Length of side 1= 9+1= 
9+1 = 10
10   Length of side 2= 8+1= 
8+1 = 9
9   Area of rectangle= 10*9= 
10*9 = 90
90   90 is the answer
Answer: D
If g and y are integers, then gy(g + y) is	Choose the correct choice.
A) Always positive  B) Always negative  C) Positive when g is positive  D) Negative when g is negative  E) It cannot be determined by the information given

Solution: Given g and y are integers, then gy(g + y)   Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..   I presume its Option E if am not missing anything.   g=-3 and y=1   gy(g + y) is positive = 6
Answer: E
What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x Choose the correct choice from the following answers
A) 64535
B) 73205
C) 79345
D) 85463
E) 84543

Solution: (73205)   5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205
Answer: B
10% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants?
Choose the correct choice
A) 4500	B) 5000	C) 3000	D) 6000	E) 5700

Solution: Let the total number of original inhabitants be x   Then, (100-25)% of (100-10)% of x = 4050   75/100 * 90/100 * x = 4050   x = 6000   Answer is 6000
Answer: D
A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?	Options:
A) 110
B) 120
C) 128
D) 143
E) 145

Solution: First Purchased = 250 Wes= 128   128
Answer: C
On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 300 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?
Choose the correct choice from the following answers:
A) 600 B) 300 C) 350 D) 400 E) 550

Solution: Let D = total distance   Traci traveled 1/3 = D/3   i.e. remaining distance = 2D/3   She traveled 1/4 th of 2D/3 = D/6   Thus:   D = (D/3) + (D/6) + 300   D = 600   600NSWER: 600
Answer: A
Nancy works 3 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 4 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?	Choose the correct choice
A) a) 3y(7x+2xy) B) b) 3x+12y C) c) 3xy(7x+2) D) d) 8x(y+3) E) e) 4x(y+8)

Solution: Payment of a week for 3 days a week = $3x   Payment of 4 weeks for 3 days a week = $3x*4 = $12x   Payment of a week for y days overtime a week 3 *4= 
3 *4 = 12
$12x   Payment of a week for y days overtime a week= $3x+$2xy   Payment of 4 weeks for y days overtime a week = ($3x+$2xy)*4   Total Earnings = $12x + ($3x+$2xy)*4 = 24x+8xy =8x(y+3)   Answer: option d) 8x(y+3)
Answer: D
One-third less than 40% of 180 is equal to:	Choices
A) 15
B) 30
C) 35
D) 40
E) 48

Solution: Lots of ways to tackle this.   40% of 180 =72   1/3 of 72= 24   So, 1/3 less than 72 is equal to  72- 24= 
 72- 24 = 48
48   Answer: 48
Answer: E
The average of 5 consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?	Pick:  A) 8  B) 10  C) 12  D) 15  E) 20

Solution: Let the numbers be x, x+2, x+4, x+6, x+8   Then, (x+ x+2+ x+4+ x+6+ x+8)/5 = 61   x = 57   Required answer is = 57+8-57= 
57+8-57 = 8
8   8nswer is 8
Answer: A
Arrange the following in a meaningful sequence :
1. Letter
2. Sentence
3. Word
4. Phrase Choose the correct choice:
A) 1, 2, 4, 3	B) 2, 1, 3, 4	C) 2, 4, 1, 3	D) 1, 3, 4, 2	E) None of these

Solution: Explanation:   A group of letters makes a word. A group of words makes a phrase. A group of phrases makes a sentence.   Thus, correct order is 1, 3, 4, 2.   ANSWER 1, 3, 4, 2
Answer: D
Brittany's income is 12 percent more than Tina's income, and Tina's income is 15 percent less than Jean's income. What percent of Jean's income is Brittany's income?
Choose the correct choice from the following.
A) 95.2% B) 91.2% C) 96.2% D) 94.2% E) 92.2%

Solution: Jean's income = 100 (assume);   Tina's income = 85 (15 percent less than Jean's income);   Brittany's income = 95.2 (12 percent more than Tina's income).   Thus, Brittany's income (95.2) is 95.2% of Jean's income (100).   95.2%nswer: 95.2%
Answer: A
Find the probability that the sum of dots appearing in two successive throws of two dice is every time 7  Choose the correct choice from the following answers
A) 1/6	B) 2/6	C) 3/6	D) 4/6	E) 5/6

Solution: No of sample space are n(s)=(6*6)= 
(6*6) = 36
36   no of even aren n(E)={(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}=6   then Probability=n(e)/n(s)=6/36 =1/6   Ans is 1/6.   1/6NSWER:1/6
Answer: A
P is a set containing 8 different positive odd numbers. Q is a set containing 7 different numbers, all of which are members of P. Which of the following statements CANNOT be true?	Answers.
A) The range of Q is even. B) The mean of P is even. C) The mean of Q is even. D) The range of P is equal to the range of Q. E) The median of Q is equal to the mean of Q.

Solution: Given: P is a set containing 8 different positive odd numbers   Easily inferred: Q is a set containing 7 differentoddnumbers   (A) The range of Q is even. - Always even, since it is a difference of two odd numbers   (B) The mean of P is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number   (C) The mean of Q is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.   (D) The range of P is equal to the range of Q.   (E) The median of Q is equal to the mean of Q   Option The mean of Q is even..
Answer: C
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Choices
A) 54	B) 62	C) 48	D) 62	E) 62

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   Answer:48
Answer: C
In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards F will he need to gain this Sunday if he wants to keep his season average above 100 yards?  Choose the correct option:
A) 101
B) 116
C) 130
D) F=131
E) F=141

Solution: Sorry the answer F=131 is F=131.
Answer: D
What percent of a day in 6 hours? Choose one:
A) 10%  B) 15%  C) 20%  D) 25%  E) 50%

Solution: Required percentage = 6/24 * 100 = 100/4= 
100/4 = 25
25%   Answer is 25%
Answer: D
The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 84, and the average of the female students’ grades was 92, how many female students took the test?	Answers
A) 8	B) 9	C) 10	D) 21	E) 24

Solution: Total Marks of male = M   Total Marks of female = F   Number of males = 8   Number of females = f   Given: (M+F)/(8+f) = 90 -------------1   Also given, M/8 = 84 Thus M = 672 ---------2   Also, F/f = 92 thus F = 92 F - --------3   Put 2 and 3 in 1: we get   (672+92f)/(8+f) = 90   solving this we get f = 24   Ans: 24
Answer: E
A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 5 a.m.? Choose the correct choice from the following options
A) 23 Minutes	B) 24 Minutes	C) 25 Minutes	D) 27 Minutes	E) None of these

Solution: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min   then from 4:00p.m-4:00 a.m =13*2= 
13*2 = 26
26 total=27   ANSWER:27 Minutes
Answer: D
The price of a T.V. set worth Rs. 10000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?  Select the correct option:
A) 9000  B) 26699  C) 96000  D) 19000  E) 26711

Solution: Money paid in cash = Rs. 1000   Balance payment = (10000 - 1000) = Rs. 9000   9000nswer: 9000
Answer: A
If n is the product of three consecutive integers, and n is divisible by 11, which of the following is not necessarily a divisor of n ?	Choose the correct choice from the following answers:  A) 990  B) 1210  C) 1716  D) 0  E) 2

Solution: IF ONE NO. IS 11 THEN OTHER CONSEQUTIVE NO. ARE   9*10*11= 
  9*10*11 = 990
990 ,10*11*12=1210 , 11*12*13 =1716   N IS NOT 0IVISOR ANY ABOVE NO =0   0
Answer: D
The cost price of 5 oranges equal to the selling price of 8 oranges. Calculate the % profit or loss.  Choose the correct choice from the following answers.
A) 38.5% B) 37.5% C) 73.5% D) 32.5% E) 31.5%

Solution: Let the cost price of 1 orange is Rs 1   Cost of 8 orange = Rs 8   Selling price of 8 orange = 5   Gain/loss = 8 - 5= 
8 - 5 = 3
3   %=3/8âˆ—100= 37.5   Answer: 37.5%
Answer: B
In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a three. You pick a card from a full playing-card deck, and success would be picking a ace with heart card.
If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
Pick one.
A) 61/312  B) 13/624  C) 325/624  D) 181/312  E) 163/625

Solution: Event(1): Probability of getting head in a flip of coin = 1/2   Event(2): Probability of getting three in a roll of dice = 1/6   Event(3): Probability of getting ace with heart in a pack of card = 1/52   Probability of winning is having exactly one successful event is:   P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)   = 1/2*5/6*51/52 +1/2*1/6*51/52 +1/2*5/6*1/52   =255/624 + 102/624 +5/624   =362/624   = 181/312   Answer :181/312
Answer: D
In a certain game, you pick a card from a standard deck of 52 cards. If the card is a clever, you win. If the card is not a clever, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a clever, and the point is to measure how many draws did it take before the person picked a clever and won. What is the probability that there will be at least four draws involved in a win, i.e. someone picking her clever on the fourth draw or later? Answers:
A) 1/2
B) 27/64
C) 11/16
D) 13/16
E) 15/16

Solution: Probability of picking a clever on any draw = 1/4   Probability of NOT picking a heart on the first draw AND on the second draw And 3rd draw = [1-(1/4)] X [1-(1/4)] X [1-(1/4)]= 3/4 X 3/4 X 3/4 = 27/64   Answer : 27/64
Answer: B
Kareem is three times as old as his son. After ten years, the sum of their ages will be 76 years. Find their present ages.	Choose the correct choice from the following:
A) 13  B) 14  C) 15  D) 16  E) 17

Solution: Sol. Let the present age of Kareem’s son be x years.   Then, Kareem’s age = 3x years   After 10 years, Kareem’s age = 3x + 10 years   and Kareem’s son’s age = x + 10 years   ∴ (3x + 10) + (x + 10) = 76   => 4x = 56 => x = 14   ∴ Kareem’s present age = 3x = 3 × 14 = 42 years   Kareem’s son’s age = x = 14 years.   Answer 14
Answer: B
Anand starts from a point P towards point Q, where PQ = 70 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
Pick.
A) (45/7) kmph
B) (60/7) kmph
C) (40/7) kmph
D) (20/3) kmph
E) (65/7) kmph

Solution: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (70-x) km   Anand traveled this x kms in 3 hours, making his speed x/3 kmph   Ram traveled the same x kms in 2 hours, making his speed x/2 kmph   So, in 6 hours:   Anand will cover=6x/3=2x km   Ram will cover6 /3= 
6 /3 = 2
2x km   Ram will cover=6x/2=3x km   And between their first meeting point and second, they both together covered a distance of 2(90-x) km.   2x+3x6 /2= 
6 /2 = 3
3x km   And between their first meeting point and second, they both together covered a distance of 2(90-x) km.   2x+3x=2(70-x)   5x=140-2x   7x=140   x=140/7 km   Anand's speed=x/3=140/(3*7)=20/3 kmph   Ans:(20/3) kmph
Answer: D
A particular parking garage is increasing its rates by 40 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month? Choose the most appropriate option.
A) 20% B) 25% C) 29% D) 33% E) 40%

Solution: Let x be the original number of days that Bob used the garage.   Let P be the original cost per day.   Let N*x be the new number of days that Bob uses the garage.   N*x*1.4P = x*P   N*x = x/1.4 which is about 0.71x, thus a 29% reduction.   The answer is 29%.
Answer: C
Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 29 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?
Select.
A) 14.5 minutes	B) 29 minutes	C) 35 minutes	D) 58 minutes	E) 87 minutes

Solution: Danny's time is 29 minutes. The time to reach halfway is 14.5 minutes.   Steve's time is 58 minutes. The time to reach halfway is 29 minutes.   The time difference is   29 - 14.5= 
  29 - 14.5 = 14.5
14.5 minutes   The answer is 14.5 minutes.
Answer: A
At what time between 4 and 5 o’clock the hands are in opposite direction? Choose the correct choice from the following:
A) 3 2/11 minutes past 4 o’clock	B) 3 5/11 minutes past 4 o’clock	C) 10 10/11 minutes past 4 o’clock	D) 10 2/11 minutes past 4 o’clock	E) 54 6/11 mintues past 4'0 clock

Solution: To be in opposite directions, they must be 30 min. spaces apart.   Minute hand will have to gain 50 min. spaces.   55 min. spaces are gained in 60 min.   50 min. spaces are gained in 60/55 x 50 min. or 54 6/11 min. Required time = 54 6/11 min. past 4 o’clock   ANSW54 6/11 mintues past 4'0 clockR:54 6/11 mintues past 4'0 clock
Answer: E
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 48 kmph, find the speed of the stream? Choose the correct choice from the following options:
A) 12 kmph  B) 13 kmph  C) 14 kmph  D) 15 kmph  E) 16 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= 48/3= 
48/3 = 16
16 kmph   ANSW16 kmphR:16 kmph
Answer: E
Each of the 9 squares shown is to contain one number
chosen from 1, 2, 3, 4, 5, 6, 7, 8, and 9. No number is to
be repeated. Suppose the sum of the 5 squares aligned
vertically on the right is 32 and that the sum of the 5
squares aligned horizontally on the bottom is 20. What
number goes in the shared corner square?	Choose the correct option.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: If x is the number in the corner square, then the sum of all the numbers in the squares is equal   to the sum of the numbers in the five squares aligned vertically plus the sum of the numbers in the   five squares aligned horizontally minus x. Hence,   1 + 2 + · · · + 9 = 32 + 20 − x.   The sum on the left is 45, so x = 52 − 45 = 7.   correct answer 7
Answer: E
In how many ways can the letters D, I, T , K , T be arranged so that the two I's are not next to each other?
Options.
A) 36  B) 48  C) 72  D) 96  E) 128

Solution: 1 D   1 I   1 G   2 T   Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60   Consider 2 Is as 1 entity and thus the number of arrangements for (TT)DGI = 4! = 24   Total allowed cases = 60-24= 
60-24 = 36
36   36 is the correct answer.
Answer: A
The bankers gain of a certain sum due 2 years hence at 10% per annum is Rs 24 .The percent worth is	Pick.
A) 387 B) 238 C) 278 D) 600 E) 281

Solution: Explanation:   T.D = (B.G * 100) / (Rate * Time)   (24*100) / (10 * 2)= 
(24*100) / (10 * 2) = 120
120.   P.W= (100 *T.600) / (Rate * Time)   = (100 * 120) /(10 * 2)= 
(100 * 120) /(10 * 2) = 600
600   Answer: 600) 600
Answer: D
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?  Choose the most appropriate option:
A) 736
B) 988
C) 999
D) 729
E) 737

Solution: Explanation:   a2 = 3136 => a = 56   56 * 4 * 3= 
56 * 4 * 3 = 672
672 – 6= 666 * 1.5= 
666 * 1.5 = 999
999   Answer: Option 999
Answer: C
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle. Choose the correct answer:
A) 10 cm
B) 15 cm
C) 20 cm
D) 18 cm
E) 24 cm

Solution: Explanation:   Let breadth = x. Then, length = 2x. Then,   (2x - 5) (x + 5) - 2x * x = 75 => 5x - 25 = 75 => x = 20.   Length of the rectangle = 20 cm.   Answer: Option 20 cm
Answer: C
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Choose the correct option:
A) 729
B) 720
C) 718
D) 750
E) 782

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 25 è x = 25 * 60 / 2= 
25 * 60 / 2 = 750
750   Answer:750
Answer: D
A man bought 40 shares of Rs. 60 at 5 discount, the rate of dividend being 12%The rate of interest obtained is
Select the correct option
A) 13.09%
B) 15.5%
C) 14%
D) 14.25%
E) 14.95%

Solution: Explanation :   Face Value of a share = Rs.60   He bought each share at Rs.60 - Rs.5 = Rs.55   Number of shares = 40   Dividend = 12 %   Dividend per share = 60×12×100=Rs.7 1/5   Total dividend = (40 × 7 1/5)   ie, He got a dividend of (40 × 7 1/5) for an investment of Rs.(40 × 55)   Interest obtained = 40×7 1/5×100/40×55=13.09%   13.09%nswer : Option 13.09%
Answer: A
Which of the following is equal to the average (arithmetic mean) of (x+1)^2 and (x-1)^2?
Select the correct option:
A) x^2  B) x^2+1  C) x^2 +4  D) x^2+2x  E) x^2+4x

Solution: Avg = [(x+1)^2 + (x-1)^2] / 2   Expanding and simplifying, (x^2 + 2x + 1 + x^2 -2x + 1 ) / 2 = x^2 + 1   Answer x^2+1.
Answer: B
A train covers a distance of 12 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?  Select the correct option:	A) 177 m	B) 189 m	C) 120 m	D) 178 m	E) 200 m

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec   = 20 m/sec.   Length of the train = 20 * 10= 
20 * 10 = 200
200 m.   Answer: 200 m
Answer: E
The ratio of the present ages of Giri and Hari is 5 : 8. 12 years hence, the ratio of their ages will be 11 : 14. Find the difference in their present ages?	Choose the most appropriate option
A) 5 years
B) 6 years
C) 3 years
D) 9 years
E) 2 years

Solution: Let the present ages of Giri and Hari be 5x and 8x years respectively.   (5x + 12) / (8x + 12) = 11/14   70x + 168 = 88x + 132 => x= 2   Difference in their ages will be the same at all times.   This difference = Difference of their present ages   = 8x - 5x = 3x 8  - 5= 
8  - 5 = 3
3x= 6 years.   Answer:6 years
Answer: B
Three candidates contested an election and received 3644 votes, 7636 votes, and 12720 votes respectively. What percentage of the total votes did the winning candidate receive?
Choose the correct choice from the following answers.
A) 53%  B) 55%  C) 57%  D) 59%  E) 61%

Solution: The total number of votes polled = (3644 + 7636 + 12720)= 
(3644 + 7636 + 12720) = 24_000
24000   The winner's percentage= 12720/24000 * 100= 
12720/24000 * 100 = 53
53%   The answer is 53%.
Answer: A
What will be the fraction of 10%
Select:
A) 1/4 B) 1/5 C) 1/10 D) 1/8 E) None of above

Solution: Explanation:   It will 10*1/100 = 1/10   Answer: Option 1/10
Answer: C
The length of a rectangle is increased by 40% while its width is halved. What is the % change in area? Choose the most appropriate option:
A) 25%	B) 30%	C) 50%	D) 65%	E) 70%

Solution: The original area is L*W   The new area is 1.4L*0.5W = 0.7*L*W   1.4 *0.5= 
  1.4 *0.5 = 0.7
0.7*L*W= L*W - 0.3*L*W   The area decreased by 30%.   The answer is 30%.
Answer: B
3x^2 + 10x - 8 =
Choose the correct choice:
A) (3x-4)(x-1)	B) (3x-4)(x+2)	C) (3x-4)(x-2)	D) (3x-2)(x+4)	E) none of above

Solution: 3x^2 - 10x - 8   = 3x^2 + 12x - 2x - 8   = 3x (x + 4) - 2 (x+4)   = (3x-2) (x+4)   Option (3x-2)(x+4)
Answer: D
Let x < 0, 0 < y < 1, z > 1. Which of the following may be false? Choose the correct choice: A) (x^2– z^2) has to be positive. B) yz can be less than one. C) xy can never be zero. D) (y^2– z^2) is always negative. E) None

Solution: Explanation :   Let's take any random value satisfying the given condition i.e x < 0, 0 < y < 1, z > 1.   Take x = -1, and z = 2   x2 - z2 -> (-1)2 - (2)2 = -3 .   Take y= 0.1,   then , yz -> (1/10)*2 = 1 /5 i.e less than 1.   According to the given condition, x and y both are non zero, so there product can't be zero.   Since, value of z will always be greater than 2 and y will always be less than 1, So, y2 - z2 will always result into a negative value.   Hence, only first option is false.   (x^2– z^2) has to be positive.nswer : (x^2– z^2) has to be positive.
Answer: A
A man can row 9 1/3 kmph in still water and finds that it takes him thrice as uch time to row up than as to row down the same distance in the river. The speed of the current is: Select.
A) 3 1/2 km/hr
B) 2 1/3 km/hr
C) 4 1/2 km/hr
D) 4 2/3 km/hr
E) None

Solution: Sol.   Let speed upstream be x kmph. Then, speed downstream = 3x kmph.   Speed in still water = 1/2(3x + x) kmph = 2x kmph.   ∴ 2x = 28/3 ⇒ x = 14/3   So, Speed upstream = 14/3 km/hr; Speed downstream = 14/hr.   Hence, speed of the current = 1/2 [14 - 14/3] km/hr = 14/3 km/hr = 4 2/3 km/hr.   Answer 4 2/3 km/hr
Answer: D
If selling price is doubled, the profit triples. Find the profit percent: Pick one:
A) 170  B) 320  C) 100  D) 280  E) 200

Solution: C   100%   Let C.P. be Rs. x and S.P. be Rx. y.   Then, 3(y - x) = (2y - x) => y = 2x   Profit = (y - x) = Rs. (2x - x) = Rs. x   Profit % = x/x * 100 = 100%.
Answer: C
The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
Choose the correct choice from the following choices:	A) 8	B) 4	C) 12	D) 16	E) 7

Solution: Explanation:   Let the two consecutive even integers be 2n and (2n + 2). Then,   (2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)   = 2(4n + 2)   = 4(2n + 1), which is divisible by 4.   Answer 4
Answer: B
What is the units digit of (5!*4! + 6!*5!)/3?  Choices:
A) 4	B) 3	C) 2	D) 0	E) 1

Solution: (5!*4! + 6!*5!)/3   =5!(4! + 6!)/3   =120 ( 24 + 720)/3   =(120 * 744)/3   = 120 * 248   Units digit of the above product will be equal to 0   Answer 0
Answer: D
If the sum and difference of two numbers are 10 and 8 respectively, then the difference of their square is:
Choose the correct choice from the following answers
A) 12
B) 28
C) 160
D) 180
E) 80

Solution: Let the numbers be x and y.   Then, x + y = 10 and x - y = 8   x2 - y2 = (x + y)(x - y) = 10 * 8= 
10 * 8 = 80
80.   ANSW80R:80
Answer: E