MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the square root of 36, divided by 6?  Choose the most appropriate option.
A) 9	B) 36	C) 122	D) 6	E) 1

Solution: Square root is a number times itself   Square root of 36=6, 6/6=1   (1)1
Answer: E
In 10 years,A will be twice as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :  Choose the most appropriate option:
A) 19 Years B) 29 Years C) 39 Years D) 49 Years E) 59 Years

Solution: Solution   Let B's present age = x years.Then,A's present age =(x +9) years.   ∴ (x + 9)+ 10 = 2 (x - 10) ⇔ x + 19 = 2x- 20 ⇔ x = 39.Answer 39 Years
Answer: C
The H.C.F. and L.C.M. of 0.63, 1.05 and 2.1  Choices
A) (i)0.20(ii)6.31 B) (i)0.21(ii)5.30 C) (i)0.21(ii)6.30 D) (i)1.21(ii)6.50 E) None of these

Solution: Explanation :   Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10.   Without decimal places, these numbers are 63, 105 and 210.   Now, H.C.F. of 63, 105 and 210 is 21.   H.C.F. of 0.63, 1.05 and 2.1 is 0.21.   L.C.M. of 63, 105 and 210 is 630.   L.C.M. of 0.63, 1.05 and 2.1 is 6.30.   ANSWER IS (i)0.21(ii)6.30
Answer: C
I flew my tiny seaplane to visit my mother. On the flight up, I flew at 140 mph. On the way home, I flew 88 mph. What was my average speed for the trip?	Choose the most appropriate option.
A) 114 mph
B) 110 mph
C) 88 mph
D) 100 mph
E) 99 mph

Solution: (140 mph +88 mph)/2= 114 mph   Correct answer is: 114 mph
Answer: A
Pradeep has to obtain 25% of the total marks to pass. He got 185 marks and failed by 25 marks. The maximum marks are	Choose the correct choice from the following answers.
A) 840
B) 600
C) 800
D) 1000
E) 900

Solution: Explanation :   Let their maximum marks be x.   Then, 25% of x = 185 + 25   =>25/100x= 210   x = (210100/25)   x= 840.   840nswer : 840
Answer: A
On what sum will the compound interest for 2 1⁄2 years at 10% amount to Rs. 31762.5?	Answers:
A) Rs.5000
B) Rs.30000
C) Rs.25000
D) Rs.20000
E) Rs.30000

Solution: Explanation:   P(1+10/100)2 × (1+(1/2×10)/100) = 31762.5   P(11/10)2 × (21/20) = 31762.5   P = (31762.5 × 20 × 10 × 10)/(21 × 11 × 11)   = (1512.5 × 20 × 10 × 10)/(11 × 11)   = (137.5 × 20 × 10 × 10)/11   = 12.5 × 20 × 10 × 10 = Rs. 25000   Answer: Option Rs.25000
Answer: C
A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?	Pick.
A) 2.15 pm	B) 2.15 am	C) 3.15 pm	D) 3.15 am	E) None of them

Solution: Suppose they meet x hours after 10 a.m. Then,   (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.   65x + 35(x-1) = 390 => 100x = 425 => x =	17/4   So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.   2.15 pmnswer is 2.15 pm.
Answer: A
2 no's are respectively 40% & 60% more than 3rdnumber. Find the ration of two numbers ? Choose the correct choice from the following
A) 4 : 5
B) 5 : 7
C) 7 : 8
D) 7 : 9
E) 7 : 11

Solution: Step 1: Let the third number is A   Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.   Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.   7 : 8
Answer: C
A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways this can be done is:
Choose the correct choice from the following options
A) 122	B) 210	C) 216	D) 217	E) 225

Solution: First step:   We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.   We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.   For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.   Second step:   We have two set of numbers:   1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:   1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.   0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96   120+96= 
120+96 = 216
216   Answer: 216.
Answer: C
A single discount equivalent to the discount series of 10%, 10% and 5% is?	Select the correct option:	A) 23.05	B) 31.95	C) 21.65	D) 23.45	E) 23.15

Solution: 100*(90/100)*(90/100)*(95/100)= 
100*(90/100)*(90/100)*(95/100) = 1_539/20 = around 76.95
76.95   100 - 76.95= 
100 - 76.95 = 23.05
23.05   23.05nswer: 23.05
Answer: A
What is the value of n if the sum of the consecutive odd intergers W from 1 to n equals 169?
Choose one:
A) 47 B) 25 C) 37 D) 33 E) 29

Solution: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.   Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.   a=1 (first term)   d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2   *On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.   But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.   Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.   It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Answer: B
The average age of the district level hockey team of eleven is 22 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ?
Choose the correct choice from the following choices.
A) 22 yrs B) 34 yrs C) 27 yrs D) 28 yrs E) 19 yrs

Solution: Total age of players in team = 22 x 11 = 242   When coach is included, total members = 12, Avg age increases by one becomes 23   Total age when coach is included = 23x12 = 276   Age of coach = 276-242= 
276-242 = 34
34 yrs.   Answer: 34 yrs
Answer: B
An aircraft is flying at a height of 3000m from the ground at an average speed of 400 km/hr while descending. It has to travel 5 kms before it can touch down the runway and start operating its break system. It will take less than 10 seconds to reach the touch down point. How far it is from the touch down point if it had been on they ground.	Select the correct option
A) 5 kms  B) 4 kms  C) 3 kms  D) 6 kms  E) none of these

Solution: answer is 4   simple Pythagoras theorem   ANSWER:4 kms
Answer: B
At what rate percent on simple interest will a sum of money double itself in 30 years? Pick one:
A) 3 1/9%
B) 3 7/3%
C) 7 1/3%
D) 5 1/3%
E) 1 1/3%

Solution: P = (P*30*R)/100   R = 3 1/3%   3 1/9%nswer: 3 1/9%
Answer: A
How many three digit numbers can having only two consecutive digits identical is	Choices
A) 153 B) 162 C) 168 D) 163 E) None of these

Solution: When 0 is the repeated digit like   100, 200, ...., 9 in number   When 0 occurs only once like   110, 220, ....., 9 in number   When 0 does not occur like   112,211, ....., 2 × (8 × 9) = 144 in number.   Hence, total = 9 + 9 + 144= 
9 + 9 + 144 = 162
162.   Answer 162
Answer: B
If m^2-8m+1=0,then m^3+m^(-3)= ?  Choose the correct option:
A) 487	B) 488	C) 489	D) 457	E) 495

Solution: here from equation 1 we will get   m^2-8m+1=0   m^2=8m-1   m=(8m-1)/m.........(1)   m=8-1/m   so m+1/m=8   now in equation 2   m^3+1/m^3   (m+1/m)(m^2 - m*1/m + 1/m^2)   (m+1/m)(m^2 - 1 + 1/m^2)   (m+1/m)(m^2 + 1/m^2 - 1)   (m+1/m){(m+1/m)^2 - 2m*1/m - 1} {since a^2+b^2=(a+b)^2-2ab}   (m+1/m){(m+1/m)^2 - 2-1}   now putting the value of m from equation 1   8(8^2-2-1)   8(64-3)   =488   ANSWER:488
Answer: B
The ratio of the radius of two circles is 2: 7, and then the ratio of their areas is? Choose the correct choice from the following options:
A) 1:7 B) 2:9 C) 1:9 D) 4:49 E) 3:4

Solution: r1: r2 = 2: 7   Î r1^2: Î r2^2   r1^2: r2^2 = 4:49   Answer: 4:49
Answer: D
A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1215. Find the number to be multiplied.  Answers
A) 130
B) 132
C) 135
D) 136
E) 138

Solution: Let the required number be x. Then,   43x – 34x = 1215 or 9x = 1215 or x = 135.   Required number = 135   ANSWER:135
Answer: C
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?  Choose the correct choice from the following options: A) 24 B) 125 C) 243 D) 504 E) 729

Solution: P=3, R=4, and T=2.   There are following cases possible:   1. Different kinf of plays:   PRT (Any combination) = 3*4*2*3!=144.   2. Two same kind of plays and one from other kind of play:   PPR (Any combination. Notice that the two P's here must be different) = C23∗4∗3!=72C32∗4∗3!=72;   PPT = C23∗2∗3!=36;   RRP = C24∗3∗3!=108   RRT = C24∗2∗3!=72   TTP = C22∗3∗3!=18   TTR = C22∗4∗3!=24   3. All three plays are of the same kind:   PPP = C^3_3*3!=6   RRR = C^3_4*3!=24   TTT is not possible because we have only two T's.   Total = 144 + 72 + 36 + 108 + 72 + 18 + 24 + 6 + 24= 
144 + 72 + 36 + 108 + 72 + 18 + 24 + 6 + 24 = 504
504.   Answer: 504.
Answer: D
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?	Options
A) 299 B) 180 C) 288 D) 127 E) 122

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer: 180
Answer: B
8597 - ? = 7429 - 4358  Select the correct option:	A) 5426	B) 5706	C) 5526	D) 5476	E) None of these

Solution: Explanation:   7429 Let 8597 - x = 3071   -4358 Then, x = 8597 - 3071   ---- = 5526   3071   ----   Answer: 5526
Answer: C
Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is	Choose the correct choice from the following options:
A) 32 years B) 36 years C) 38 years D) 40 years E) None

Solution: Solution   Let Rajan's present age be x years. Then, his age at the time of marriage	=(x-8) years.   Therefore	x= 6/5(x-6)   5x = 6x-48   x=48.   Rajan's sister's age at the time of his marriage=(x-8)-10	=(x-18)=30   Rajan's sister's present age	=(30+8)= 
(30+8) = 38
38 years.   Answer 38 years
Answer: C
Which of the following is closer to (20!+19!)/(20!-19!)?	Options
A) 11
B) 13
C) 1
D) 3
E) 7

Solution: Notice that 20! = (20)(19!),   (20!+19!)*(20!-19!)=[19!(20+1)]*[19!(20-1)]   = 21/19   ≈ 1   Answer: 1
Answer: C
Let X be the smallest positive integer such that 28 and 42 are factors of 678 - X, so the value of X is:
Pick.
A) 28	B) 48	C) 6	D) 62	E) 34

Solution: You can simply check which of the possible values for X will make 678-X divisible by 28 and 42 simultaneously.   The only possible value is X = 6 (because   678 - 6= 
  678 - 6 = 672
672= 28*24 = 42*16).   Answer 6
Answer: C
If |8y−3|=|2y+7|, which of the following could be a value of y?  Choose the correct choice from the following answers
A) 1  B) 5/3  C) 2/5  D) -2/3  E) -1

Solution: 8y − 3 = 2y + 7 or 8y − 3 = -2y - 7   6y = 10 or 10y = -4   y = 5/3 or y = -2/5   Answer: 5/3
Answer: B
A sum fetched total simple interest of 4016.25 at the rate of 10 p.c.p.a. in 5 years. What is the sum?  Choose the correct option
A) 8925	B) 8032.5	C) 4462.5	D) 8900	E) None of these

Solution: Let the sums be P.   Now, 50% of P = 4016.25   or, P = 8032.5   Answer 8032.5
Answer: B
The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
Options:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Explanation:   P(1+20/100)n>2P =>(6/5)n>2.   Now,(6/5x6/5x6/5x6/5)>2.   So, n=4years.   ANSWER IS 4
Answer: B
An empty fuel tank is filled with brand Z gasoline. When the tank is 3/4 empty, it is filled with brand X gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand X gasoline. At this time, what percent of the gasoline in the tank is brand Z?  Choose the correct option: A) 41% B) 42% C) 43% D) 43.75% E) 44%

Solution: Work with fraction of brand Z in the tank.   1st step: brand Z is 1   2nd step: brand Z is 1/2   3rd step: brand Z is (3/4)*(1/2) + 1/2 = 7/8   4th step: brand Z is (1/2)*(7/8) = 7/16 = 43.75%   Answer (43.75%)
Answer: D
How many times the keys of a typewriter have to be pressed in order to write first 400 counting numbers? Choose the correct choice from the following answers:
A) 1200	B) 1092	C) 1082	D) 1192	E) 1292

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 400= 301 * 3= 
301 * 3 = 903
903   -----------   1092   ANSWER:1092
Answer: B
A train 710 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?	Choose one
A) 2898 B) 277 C) 500 D) 297 E) 590

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (710 + x)/60 = 65/3   x = 590 m.   Answer: 590
Answer: E
Jane makes toy bears. When she works with an assistant, she makes 53 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?	Choose the correct choice from the following options:  A) 20%  B) 70%  C) 100%  D) 180%  E) 200%

Solution: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears/hr ([40 bears * 1.53] / [40 hrs * .90]).   [(1.7 - 1)/1] * 100% = 70%   ANSWER:70% (1.7 - 1)/1  * 100= 
 (1.7 - 1)/1  * 100 = 70
70%   ANSWER:70%
Answer: B
A man takes 5hr 45min in walking to certain place and riding back. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is? Choices
A) 7 hr 45 min  B) 7 hr 15 min  C) 6 hr 45 min  D) 6 hr 15 min  E) 6 hr 25 min

Solution: Let x be the speed of walked   Let y be the speed of ride   Let D be the distance   Then D/x + D/y = 23/4 hr -------------------(1)   D/y + D/y = 23/4 – 2 hr   D/y = 15/8 ----------------------------------(2)   substitute 2 in 1   D/x + 15/8 = 23/4   D/x = 23/4 -15/8 =46-15/8 =31/8   Time taken for walk one way is 31/8 hr   time taken to walk to and fro is 2*31/8 = 31/4 hr   =7 hr 45 min   7 hr 45 minnswer : 7 hr 45 min.
Answer: A
Two sets of 7 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?	Options:  A) 24  B) 17  C) 28  D) 42  E) it cannot be determined from the information given.

Solution: A=(1,2,3,4,5,6,7), sum of this=28   B=(7,8,9,10,11,12,13), sum of this=70   The differenct between   70-28= 
  70-28 = 42
42   Hence,42 is the answer i.e.42
Answer: D
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 33% iodine solution? Choose the correct choice from the following choices:	A) 35	B) 49	C) 100	D) 105	E) 122

Solution: Solution 1:   Assume the iodine solution to be mixed = x lts.   Iodine = 0.4x lts, Water = 0.6x lts.   Solution 2: 35 liters of a 20% iodine solution   Iodine = 7 lts, Water = 28 lts.   Total iodine = 0.4x + 7   Total water = 0.6x + 28   The resultant is a 35% idoine solution.   Hence (0.4x + 7) / (x + 35) = 33/100   40x + 700 = 33x + 1155   7x = 855   x = 122 lts   Correct Option: 122
Answer: E
The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle?  Pick one
A) 432 sq m
B) 363 sq m
C) 452 sq m
D) 428 sq m
E) 528 sq m

Solution: 2(3x + x) = 88   l = 33 b = 11   lb = 33 * 11= 
33 * 11 = 363
363   ANSWER:363 sq m
Answer: B
A Cuban cigar would cost 2 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?  Pick
A) 17.7$. B) 15.7$. C) 25.5$. D) 35$. E) 37.4$.

Solution: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.   From the given data we know French cigar < Cuban cigar < Arabic cigar   and each is more expensive 1.5 times. Therefore eliminate options C,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know A cannot be the answer.   Therefore 15.7$. is the answer.
Answer: B
Find the average of first 40 natural numbers.  Choose the most appropriate option
A) 20.5
B) 18
C) 19.5
D) 19
E) 20

Solution: Sum of first n natural numbers = n( n+1)/2   So, sum of first 40 natural numbers = 40*41/2= 
40*41/2 = 820
820   Required average=820/40= 
820/40 = 41/2 = around 20.5
20.5   20.5NSWER:20.5
Answer: A
If an item that originally sold for o dollars was marked up by m percent and then discounted by n percent, which of the following expressions represents the final price of the item? Select:  A) (10,000o + 100o(m – n) – mno)/10,000  B) (10,000o + 100o(n – m) – mno)/10,000  C) (100o(m – n) – mno)/10000  D) (100o(n – m) – mno)/10000  E) 10000 /(m – n)

Solution: Assume o=100, m=10, n=10. So final price is 99. Now put these value each option. Only option (10,000o + 100o(m – n) – mno)/10,000 will give right answer.
Answer: A
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is?  Choose one:
A) Rs. 3900
B) Rs. 4900
C) Rs. 4980
D) Rs. 5000
E) Rs. 5900

Solution: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.   Then, 10x = 4y or y =	5	x.   2   15x + 2y = 4000   15x + 2 x	5	x = 4000   2   20x = 4000   x = 200.   So, y = 5	x 200 = 500.   2   Hence, the cost of 12 chairs and 3 tables = 12x + 3y   = Rs. (2400 + 1500)   = Rs. 3900.   Rs. 3900)
Answer: A
A person want to give his money of $2700 to his 3 children A,B,C in the ratio 5:6:9. What is the A+C share? Options:
A) $1890
B) $2002
C) $3500
D) $1500
E) $5640

Solution: $1890's share = 2700*5/20= 
2700*5/20 = 675
$675   C's share= 2700*9/20= 
2700*9/20 = 1_215
$1215   $1890+D= $1890   $1890nswer is $1890
Answer: A
An article when sold at a gain of 5% yields Rs. 15 more than when sold at a loss of 5%. The cost price of the article is:	Choose the correct choice from the following options.
A) Rs. 200	B) Rs. 150	C) Rs. 80	D) Rs. 64	E) None of these

Solution: 10/100 × x = 15 ⇒ x=150   As the loss and profit both are earned on the cost price.   Answer: Rs. 150
Answer: B
In what time will a train 110 m long cross an electric pole, it its speed be 144 km/hr? Select:
A) 2.75 sec	B) 4.25 sec	C) 5 sec	D) 12.5 sec	E) 6 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 110/40= 
110/40 = 11/4 = around 2.75
2.75 sec.   2.75 secNSWER:2.75 sec
Answer: A
Simplify (212 * 212 + 312 * 312 ) Pick:
A) 132288
B) 142088
C) 142188
D) 142288
E) None of these

Solution: Explanation:   Trick: Above equation can be solved by using following formula   (a2+b2)=1/2((a+b)2+(a−b)2)   Option 142288
Answer: D
The combined salaries of three brothers is $45,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?
Choose the correct choice from the following choices: A) 10,000 B) 12,000 C) 15,000 D) 20,000 E) 22,000

Solution: Mr. Small = x;   Mr. Middle = 3/2*x;   Mr. Big = 2x.   x + 3/2*x + 2x = 45 --> x=10   10,000nswer: 10,000
Answer: A
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 1988, the price of commodity X was 4.20 and that of Y was 6.30, in which year will commodity X cost 40 paise more than commodity Y? Select the correct option
A) 1997 B) 1998 C) 1999 D) 2000 E) None of these

Solution: Suppose in ‘n’ years the price of comodity X will be more by 40 paise than that of commodity Y.   ∴ 420 + 40n – 630 – 15n = 40   or, 25n – 210 = 40   or, 25n = 250   or, n = 250⁄25 = 10 years.   Answer 1998
Answer: B
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?	Choose the correct choice from the following options.
A) 13.1 sec	B) 12.1 second	C) 22.1 sec	D) 32.1 sec	E) 13.2 sec

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/20= 
242/20 = 121/10 = around 12.1
12.1 sec.   Answer:12.1 second
Answer: B
A certain team consists of 5 professors and 4 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)
Choose the correct choice from the following: A) 74 B) 80 C) 86 D) 92 E) 98

Solution: The total number of ways to form a group of 3 from 9 people is 9C3 = 84   The number of ways to form a group without a professor is 4C3 = 4   The total number of ways to form a valid group is   84 - 4= 
  84 - 4 = 80
80.   The answer is 80.
Answer: B
The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places? Choose the correct answer.
A) 23.56	B) 23.59	C) 23.76	D) 23.12	E) 23.57

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm   i.e. 4a = 60   A = 15   Diameter of the semicircle = 15 cm   Circimference of the semicircle   = 1/2(∏)(15)   = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places   Answer: 23.57
Answer: E
Which of the following could be the sum of the reciprocals of two different prime numbers?  Choose the most appropriate option.
A) 7/13
B) 10/12
C) 11/30
D) 23/50
E) 19/77

Solution: Here, the condition is that there should be two different prime nos.   A 13 = 13 x 1 ( 1 is not a prime number)   B 21 = 7 x 3 ( both 7 and 3 are prime nos)   C 30 = 10 * 3 or 5* 6 ( It can be written both ways, but 10 and 6 are not prime nos)   D 50 = 10 * 5 ( 10 is not a prime number)   E 77 = 11 * 7 ( both are prime numbers)   Options A, C, D are eliminated.   We are left with options B and E.   1/11 + 1/7 = 18/77 and not 19/77. Hence this option is eliminated.   Option 10/12 is the correct
Answer: B