mathewhe/aqua_rat huggingface dataset:
Question: A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive). Which of the following CANNOT be the value of any one of the unknowns?
(A)  13
(B)  12
(C)  11
(D)  10
(E)  5
Rationale: VERITAS PREPOFFICIAL SOLUTION:
The question gives us concrete information about mean – it is 10 – but not about median – it is between 7 and 8 (exclusive). What can we say about median from this? That it cannot be 7 or 8 but anything in between. But we know that the list has all integers. When we have even number of integers, we know that the median is the average of the middle two numbers – when all are placed in increasing order. So can the average of the two middle numbers be, say, 7.1? Which two positive integers can average to give 7.1? None! Note that if the average of two integers is a decimal, the decimal must be (some number).5 such as 7.5 or 9.5 or 22.5 etc. This happens in case one number is odd and the other is even. In all other cases, the average would be an integer.
Since the median is given to be between 7 and 8, the median of the list of the six positive integers must be 7.5 only.
Now we know that the mean = 10 and median = 7.5
Method 1: Algebra/Logic
Let’s try to solve the question algebraically/logically first.
There are 6 elements in the list. The average of the list is 10 which means the sum of all 6 elements = 6*10 = 60
4 + 5 + 24 + x + y + z = 60
x + y + z = 27
Median of the list = 7.5
So sum of third and fourth elements must be 7.5 * 2 = 15
There are two cases possible:
Case 1: Two of the three integers x, y and z could be the third and the fourth numbers. In that case, since already 4 and 5 are less than 7.5, one of the unknown number would be less than 7.5 (the third number) and the other two would be greater than 7.5.
The sum of the third and fourth elements of the list is 15 so
15 + z = 27
z = 12
So, two numbers whose sum is 15 such that one is less than 7.5 and the other greater than 7.5 could be
5 and 10
6 and 9
7 and 8
x, y and z could take values 5, 6, 7, 8, 9, 10 and 12.
Case 2: The known 5 could be the third number in which case one of the unknown numbers is less than 5 and two of the unknown numbers would be more than 7.5.
If the third number is 5, the fourth number has to be 10 to get a median of 7.5. Hence, 10 must be one of the unknown numbers.
The sum of the other two unknown numbers would be 27 – 10 = 17.
One of them must be less than 5 and the other greater than 10. So possible options are
4 and 13
3 and 14
2 and 15
1 and 16
x, y and z could take various values but none of them could be 11
Answer (C)
Answer: (C)  11
Question: If the sum of five numbers is between 100,000 and 101,000, then the average (arithmetic mean) of the five numbers could be which of the following?
(A) 20,010
(B) 25,010
(C) 30,010
(D) 35,010
(E) 40,010
Rationale: 100000/5=20000
101000/5=20200
Only A fits in between these two limits.
Answer: A
Answer: (A) 20,010
Question: A watch was sold at a loss of 10%. If it was sold for Rs.210 more, there would have been a gain of 4%. What is the cost price?
(A) s.1000
(B) s.1009
(C) s.1007
(D) s.1006
(E) s.1500
Rationale: Explanation:
90%
104%
--------
14% ---- 210
100% ---- ? => Rs.1500
Answer:E
Answer: (E) s.1500
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second?
(A) 1234
(B) 1567
(C) NO =1349
(D) 1456
(E) 1356
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) NO =1349
Question: A woman is 4 times as old as her daughter. In 3 years she will be 3 times as old as her daughter. How old is the woman now?
(A) 3 years
(B) 6 years
(C) 12 years
(D) 24 years
(E) 36 years
Rationale: Let Woman's present age = w
and daughter's present age = d
w= 4d --- equation 1
w+3 = 3(d+3)
=>w = 3d +6 --- equation 2
From 1 and 2 , we get
d=6
w=24
Answer D
Answer: (D) 24 years
Question: If P is a prime number greater than 3, find the remainder when P^2 + 15 is divided by 12.
(A) 6
(B) 4
(C) 0
(D) 8
(E) 7
Rationale: Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 15 = 36N^2 + 12N + 1 + 15 = 36N^2 + 12N + 12 + 4
If P = 6N-1, then P^2 + 15 = 36N^2 - 12N + 1 + 15 = 36N^2 - 12N + 12 + 4
When divided by 12, it must leave a remainder of 4.
The answer is B.
Answer: (B) 4
Question: A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 84 km downstream.
(A) 4 hours
(B) 5 hours
(C) 6 hours
(D) 7 hours
(E) 8 hours
Rationale: Explanation:
It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.
Lets see the question now.
Speed downstream = (16 + 5) = 21 kmph
Time = distance/speed = 84/21 = 4 hours
ANSWER IS A
Answer: (A) 4 hours
Question: The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 60 feet on a side. What will be the volume of the new building in cubic feet?
(A) 3,937,500 cubic feet
(B) 6,619,898 cubic feet
(C) 11550√3 cubic feet
(D) 15,750√3 cubic feet
(E) 3,937,500√3 cubic feet
Rationale: Volume of the Hexagon with side 200 and height 70 = Area * height
= 6*(sqrt(3)/4)(200^2)(70)
Volume of the center bull's eye that is similar in shape of a hexagon but side 60
= 6 * (sqrt(3)/4)(60^2)*70
Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(60^2)*70=6,619,898
Answer is B
Answer: (B) 6,619,898 cubic feet
Question: Abhishek starts to paint a fence on one day. On the second day, two more friends of Abhishek join him. On the third day 3 more friends of him join him and so on. If the fence is completely painted this way in exactly 20 days, then find the number of days in which 10 girls painting together can paint the fence completely, given that every girl can paint twice as fast as Abhishek and his friends(Boys)? (Assume that the friends of Abhishek are all boys).
(A) 20
(B) 40
(C) 45
(D) 77
(E) 87
Rationale: Number of men working on first day = 1
Number of men working on second day = 3
Number of men working on second day = 6 and so on..
Total number of boys till the end of the work = [n(n + 1) (n + 2)] / 6
= [20 x 21 x 22] / 6 = 1540
Given that every girl paints twice as fast as Abhishek’s friends.
Hence, 20 girls work is being done.
Thus, the number of days taken to paint the fence = 1540/20 = 77.
ANSWER:D
Answer: (D) 77
Question: If the sum of two numbers is 22 and the sum of their squares is 460, then the product of the numbers is
(A) 40
(B) 44
(C) 12
(D) 88
(E) 48
Rationale: according to the given conditions x+y = 22
and x^2+y^2 = 460
now (x+y)^2 = x^2+y^2+2xy
so 22^2 = 460 + 2xy
so xy = 24/2 =12
ANSWER:C
Answer: (C) 12
Question: Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 10 scones must be equal to which of the following?
(A) Y/4
(B) 200/Y
(C) 100Y/(6X)
(D) XY/200
(E) Y/(5X)
Rationale: Rachel eats 4 scones/10 minutes = 2/5 scones per minute
The time for Rachel to eat 1 scone is 5/2 minutes.
The time for Rachel to eat Y scones is 5Y/2 minutes.
The time for Henry to eat X scones is 5YX/200 minutes.
The time for Henry to eat 1 scone is 5Y/200 minutes.
The time for Henry to eat 10 scones is 50Y/200 = Y/4 minutes.
The answer is A.
Answer: (A) Y/4
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 337
(B) 375
(C) 297
(D) 266
(E) 291
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: B
Answer: (B) 375
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.62000?
(A) 81000
(B) 78468.75
(C) 81008
(D) 81066
(E) 81022
Rationale: 62000* 9/8 * 9/8 = 78468.75
Answer:B
Answer: (B) 78468.75
Question: A train 110 m long is running with a speed of 80 km/h. In how many seconds will the train pass a man who is running at 8 km/h in the direction opposite to that in which the train is going?
(A) 3.5
(B) 4.5
(C) 5.5
(D) 6.5
(E) 7.5
Rationale: The speed of the train relative to the man = 80 + 8 = 88 km/h.
88000 m/h * 1h/3600 s = (880/36) m/s
(110 m) / (880/36 m/s) = (110 * 36) / 880 = 36/8 = 4.5 seconds
The answer is B.
Answer: (B) 4.5
Question: The arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
(A) 10.5
(B) 11
(C) 11.5
(D) 12
(E) 12.5
Rationale: The value which isexactlytwo SD less than the mean is:mean-2*SD=14.5-2*1.5=11.5.
Answer: C.
Answer: (C) 11.5
Question: An company has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?
(A) 10
(B) 12
(C) 15
(D) 24
(E) 30
Rationale: An company has 6 employees;for male 1C1 = 1 ........ A
foe female = 5C2 = 10.........B
total = 10*1
= 10 - answer=A
Answer: (A) 10
Question: A person takes 5hrs 45 min in walking to a place and ridingback. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is?
(A) 6 hours 23 min
(B) 6 hours 40 min
(C) 7 hours
(D) 7 hours 45 min
(E) 8 hours
Rationale: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
In fact, you can do all these calculations mentally and save a lot of time
which will be a real benefit for you.
D
Answer: (D) 7 hours 45 min
Question: How many different three letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
(A) 59
(B) 11!/(2!*2!*2!)
(C) 56
(D) 54
(E) 11!/(3!*2!*2!*2!)
Rationale: E- -R
We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.
We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.
2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.
Total = 56 + 3 = 54.
Answer:D
Answer: (D) 54
Question: The cost of carpeting a room 18m long with a carpet 75cm wide at 45 paise per meter is Rs.81. The breadth of the room is:
(A) 7m
(B) 7.5m
(C) 5.5m
(D) 6.5m
(E) 8.5m
Rationale: Length of the carpet= Total cost/ rate/m= 8100/45=180m
Area of the carpet= 180*75/100= 135m2
Breadth of the room = (Area/ length)= 135/18= 7.5m
ANSWER:B
Answer: (B) 7.5m
Question: A bus has 40 seats and the passengers agree to share the total bus fare among themselves equally. If the total fair is 80.67 , find the total no of the seats unoccupied
(A) 34
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: passengers will occupy 3 seats, per head amount payable will be 26.89. Rupees 80.67 can not be divisible other than 3
so the, Number of occupied seats will be 3
unoccupied seats will be 40-3=37
ANSWER:D
Answer: (D) 37
Question: Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent Z of the lights that are on are supposed to be off?
(A) 22(2/9)%
(B) 16(2/3)%
(C) 11(1/9)%
(D) 10%
(E) 5%
Rationale: Is the Answer D.
let me try..
Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN
Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20
Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF
Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON
So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80
From here we get SO = 20
we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.
So (8/80)*100 Z= 10%.D
Answer: (D) 10%
Question: Ferrari S.P.A is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has employed great success. Rohit once bought a Ferrari. It could go 4 times as fast as Mohan’s old Mercedes. If the speed of Mohan’s Mercedes is 35 km/hr and the distance traveled by the Ferrari is 490 km, find the total time taken for Rohit to drive that distance.
(A) 3.5
(B) 3.9
(C) 3.2
(D) 3.1
(E) 3.7
Rationale: As Ferrari's speed is four times that of the mercedes, Its speed is 35 x 4 = 140
So time taken by the ferrari = 490 / 140 = 3.5 Hours
Answer:A
Answer: (A) 3.5
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 2882
(C) 2781
(D) 2771
(E) 9121
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer: A
Answer: (A) 3630
Question: The table below shows how many coaches work with each of the major sports teams at Kristensen School. Although no single coach works with all three teams, 3 coaches work with both the Track and Tennis teams, 2 coaches work with both the Track and Baseball teams, and 1 coach works with both the Tennis and Baseball teams. How many different coaches work with these three teams?
Sports No of coaches
Track 9
Tennis 5
Baseball 4
(A) 6
(B) 9
(C) 11
(D) 12
(E) 17
Rationale: X = 9 + 5 + 4 - (3 + 2 + 1) = 12
Answer is D
Answer: (D) 12
Question: How many quarters are equal to 3 dollars?
(A) 1
(B) 8
(C) 12
(D) 9
(E) 7
Rationale: 3*4 = 12 quarters
Answer : C
Answer: (C) 12
Question: There are 13 South American countries, Annry has won a ticket to fly from Denver to one South American country and then directly to another South American Country before returning home to Denver again. Assuming there are four airports in each country, how many flights paths can Annry choose from?
(A) 13.12.11.10.4.4.
(B) 13.12.11.10.4
(C) 13.12.4.4.
(D) 13.12.4
(E) 13.13.13.13
Rationale: flights paths can Annry choose from There are 13 ways to chose the first destination,
then, 12 ways to chose next destination, with option of 4 airports (13x4)
then, to return he has 4 options to chose the airports
Thus, 13*12*4*4 ways.
Using permutations:
If the solution had written 13P1 instead of 13C1 it won't matter. As per the definition - making arrangements of the combinations gives permutations.
Since there are no arrangement for 1 item, permutationscombinations are equal.C
Answer: (C) 13.12.4.4.
Question: In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?
(A) 22 years
(B) 77 years
(C) 66 years
(D) 55 years
(E) 44 years
Rationale: T = (100 * 16500)/(15 * 5000) = 22 years.Answer:A
Answer: (A) 22 years
Question: Joanna buys an article for rs.13.00 and sells it for rs.14.00. Find her gain %.
(A) 8.32%
(B) 4%
(C) 7.69%
(D) 16%
(E) 5.36%
Rationale: sol. cp=rs13.00, sp=rs 14.00
gain=rs(14.00 –13.00)=rs1.00
so gain%={(1.00/13.00)*100}=4%
Answer is C.
Answer: (C) 7.69%
Question: A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 15 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?
(A) 450.
(B) 459.
(C) 432.
(D) 502.
(E) 522.
Rationale: Pastry is divided in 15 customers equally. So,total number of pastry must be a multiple of 15
Only option A satisfies the condition, and hence is the answer
Answer: (A) 450.
Question: The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 10 terms of the sequence?
(A) 201/100
(B) 99/100
(C) 100/101
(D) 1/10000
(E) 10/11
Rationale: Easy task and accomplish
X1=1-1/2
x2=1/2-1/3
x3=1/3-1/4
.....
x10=1/10-1/11
sum=X1+X2+X3+....X10=1-1/2+1/2-1/3+.......1/99-1/100+1/10-1/11=1-1/11=10/11
E is the answer
Answer: (E) 10/11
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 3
(B) 4
(C) 1
(D) 5
(E) 2
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
ANSWER:A
Answer: (A) 3
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is?
(A) 78
(B) 54
(C) 36
(D) 34
(E) 23
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (180 + 180)/12 => x = 15
Speed of each train = 15 m/sec.
= 15 * 18/5 =54 km/hr.
Answer: Option B
Answer: (B) 54
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
(A) 6 months
(B) 3 months
(C) 2 months
(D) 8 months
(E) 9 months
Rationale: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.
So, B joined for 8 months.
Answer: D
Answer: (D) 8 months
Question: If (1-x)y=y, which of the following must be true?
(A) x=-0 or y=0
(B) x=-1 or y=0
(C) x=1 or y=1
(D) x=-1 or y=-1
(E) x=0 or y=1
Rationale: We have (1-x)y=y.
If x=0, y=y. True
If y=0, (1-x)*0=0 True
So, A will be the answer.
Answer: (A) x=-0 or y=0
Question: The average (arithmetic mean) of eight numbers is 41.5. If the sum of half of these numbers is 154.4, what is the average of the other half?
(A) 39.9
(B) 41.1
(C) 44.4
(D) 49.9
(E) 56.6
Rationale: The average of this half is 154.4/4 = 38.6
This is 2.9 below the overall average, thus the average of the other half of the numbers must be 2.9 above the overall age, that is 41.5+2.9 = 44.4
The answer is C.
Answer: (C) 44.4
Question: Find a sum for 1st 9 prime number's?
(A) 25
(B) 28
(C) 30
(D) 34
(E) 100
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23) = 100
Note: 1 is not a prime number
Option E
Answer: (E) 100
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 8
(B) 10
(C) 12
(D) 13
(E) 15
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: In Town X, 64 percent of the population are employed, and 44 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 25%
(C) 32%
(D) 31%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 44 are employed males, hence 20% are employed females.
(employed females)/(total employed people)=20/64=1/4=31%
Answer: D.
Answer: (D) 31%
Question: Find out the wrong number in the series.
6, 12, 48, 100, 384, 768, 3072
(A) 768
(B) 384
(C) 100
(D) 488
(E) 12
Rationale: Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 12
4th term = (3rd term) x 2 = 48 x 2 = 96.
6th term = (5th term) x 2 = 384 x 2 =768.
4th term should be 96 instead of 100.
ANSWER:C
Answer: (C) 100
Question: John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?
(A) 1/2
(B) 1/3
(C) 1/5
(D) 2/15
(E) 4/15
Rationale: John will run farther if he runs at 5 mph and Amanda runs at 4 mph or 3 mph.
In this case, P(John runs farther) = 1/3 * 2/5 = 2/15
John will run farther if he runs at 4 mph and Amanda runs at 3 mph.
In this case, P(John runs farther) = 1/3 * 1/5 = 1/15
P(John runs farther) = 2/15 + 1/15 = 3/15 = 1/5
The answer is C.
Answer: (C) 1/5
Question: 70 is increased by 50%. Find the final number.
(A) 100
(B) 110
(C) 105
(D) 30
(E) 160
Rationale: Final number = Initial number + 50%(original number) = 70 + 50%(70) = 70 + 35 = 105.
Answer C
Answer: (C) 105
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
(A) 10 Yrs
(B) 20 yrs
(C) 30 yrs
(D) 35 yrs
(E) 40 yrs
Rationale: Option A
Explanation:
100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
ANSWER B
Answer: (B) 20 yrs
Question: The product Z of two prime numbers is between 16 and 40. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 12 but less than 30 then what is Z?
(A) 21
(B) 22
(C) 28
(D) 35
(E) 39
Rationale: The smallest possible product is 39 which is 3*13.
All other products are too big.
The answer is E.
Answer: (E) 39
Question: If SAGE is coded as 4657 and COT is coded as 333. How is GATE coded?
(A) 5637
(B) 5367
(C) 5763
(D) 6573
(E) 6753
Rationale: g-5 a-6 e-7 from the code gate
t - 3 from bat
ANSWER:A
Answer: (A) 5637
Question: It is required to seat 4 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
(A) 572
(B) 578
(C) 570
(D) 576
(E) 577
Rationale: Total number of candidates = 4 + 4 = 8. In the row of 8 positions, the even places are 2nd, 4th, 6th and 8th.
Now, number of even places = 4.
Number of girls to occupy the even places = 4.
Even places can be filled = P (4, 4) ways.
Number of boys = 4.
The remaining 4 places can be filled by 4 boys = P (4, 4) ways
By the fundamental principle of counting:
The required number of seating arrangements
P(4, 4) x P(4, 4) = 4! x 4! = 24 x 24 = 576
ANSWER:D
Answer: (D) 576
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 17 km/hr
(B) 89 km/hr
(C) 36 km/hr
(D) 89 km/hr
(E) 82 km/hr
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: C
Answer: (C) 36 km/hr