mathewhe/aqua_rat huggingface dataset:
Question: What is the least integer that is a sum of four different prime numbers each greater than 40?
(A) 178
(B) 180
(C) 182
(D) 184
(E) 186
Rationale: The sum of the four smallest primes greater than 40 is 41+43+47+53=184.
The answer is D.
Answer: (D) 184
Question: A theater box office sold an average (arithmetic mean) of 68 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 80, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?
(A) 2:3
(B) 1:4
(C) 5:6
(D) 7:11
(E) 3:7
Rationale: Deviation from the mean for the daytime staff = 80 - 68 = 12.
Deviation from the mean for the evening staff = 68 - 60 = 8.
Thus, the ratio of the number of daytime staff members to the number of evening staff members is 8:12 = 2:3.
The answer is A.
Answer: (A) 2:3
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length
(A) 12
(B) 12.1
(C) 13
(D) 14
(E) 15
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: Option B
Answer: (B) 12.1
Question: The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 5600 for a computer table, then what was the cost price of the computer table?
(A) Rs. 4480
(B) Rs. 5275
(C) Rs. 6275
(D) Rs. 6725
(E) None of these
Rationale: CP = SP * (100/(100 + profit%))
= 5600(100/125) = Rs. 4480.
ANSWER:A
Answer: (A) Rs. 4480
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 10 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
(A) 35 7/8
(B) 36
(C) 34 2/7
(D) 34 5/7
(E) 42 6/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 10 tons of cement, then we'll get 10/7*30 = 42 6/7 tons of mixture.
Answer: E.
Answer: (E) 42 6/7
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
(A) Rs.45
(B) Rs.78
(C) Rs.44
(D) Rs.40
(E) Rs.55
Rationale: Explanation:
π (152 - 132) = 176
176 * 1/4 = Rs.44
ANSWER IS C
Answer: (C) Rs.44
Question: When d is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when d + y is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: In my view the answer should be C
d/5 has Remainder=3 -> d = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
Answer: (C) 2
Question: (1.2)(power 3) - (0.9)(power 3)/ (1.2)(power 2) + 1.08+ (0.9)(power 2) is:
(A) 0.68
(B) 0.6
(C) 0.8
(D) 0.3
(E) None of them
Rationale: Given expression
= (1.2) (power 3) - (0.9)(power 3) / (1.2)(power 2) + (1.2 x 0.9) + (0.9)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (1.2 - 0.9)
= 0.3
Answer is D
Answer: (D) 0.3
Question: The mean of (54,823)^2 and (54,825)^2 =
(A) (54,821)^2
(B) (54,821.5)^2
(C) (54,820.5)^2
(D) (54,824)^2 + 1
(E) (54,821)^2 – 1
Rationale: 54823^2 = (54824-1)^2 = 54824^2 + 1^2 - 2*54824*1
54822^2 = (54824+1)^2 = 54824^2 +1^2 + 2*54824*1
Taking the average of above 2 , we get (54824)^2 +1
hence the answer is D
Answer: (D) (54,824)^2 + 1
Question: The product of the prime integers between 23 and 30, inclusive, is:
(A) 50! – 40!
(B) 99,029
(C) 2,303
(D) 2,021
(E) 667
Rationale: only prime number bet ween 23 and 30 inclusive are 23 and 29
thus 23*29 = 667
Ans: E
Answer: (E) 667
Question: Find the total no of divisors of 1728 (including 1 and 1728)
(A) 33
(B) 28
(C) 99
(D) 27
(E) 18
Rationale: Direct formula from our lesson on factors. Click Here.
The number of factors or divisors of a number N=ap.bq.cr...N=ap.bq.cr... = (p+1).(q+1).(r+1)... where a, b, c ... prime numbers.
1728 = 26×3326×33
So total number of divisors = (6 + 1).(3 + 1) = 28
Answer:B
Answer: (B) 28
Question: In a rectangular coordinate system, what is the area of a triangle whose vertices have the coordinates (4, 0), (6, 3), and (6, -3)?
(A) 7.5
(B) 7
(C) 6.5
(D) 6
(E) 5.5
Rationale: Area of the triangle = 1/2*base*height.
Here base = Distance between (6,3) and (6,-3) => 3-(-3) = 6
Height = distance between the base (6,0) and 4,0 => 2
Area = 1/2*6*2 = 6.
ANSWER:D
Answer: (D) 6
Question: How many numbers are divisible by 4 between 1 and 100?
(A) 25
(B) 24
(C) 23
(D) 22
(E) 20
Rationale: Numbers divisible by 4 till 100=(100/4)=25
But we should not consider 100 as we are asked to find the numbers between 1 and 100 which are divisible by 4.
so answer is 24 numbers.
Answer is option B
Answer: (B) 24
Question: The function f is defined for each positive three-digit integer n by f(n)=2x3y5zf(n)=2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80
Rationale: Soln:-
m=xyz
v=pqr
m-v = 100(x-p) + 10(y-q) + (z-r)............................(1)
f(m)= 2^x*3^y*5^z
f(v)= 2^p*3^q*5^r
Given that,
f(m) = 9 f(v)
=> 2^x*3^y*5^z = 9* 2^p*3^q*5^r
=> 2^x*3^y*5^z = 3^2*2^p*3^q*5^r
=> 2^x*3^y*5^z = 2^p*3^(q+2)*5^r
=> 2^[x-p]*3^[y-q-2]*5^[z-r] = 1
=> 2^[x-p]*3^[y-q-2]*5^[z-r] = 2^0*3^0*5^0
(x-p)=0
(z-r)=0
(y-q)=2
Substituting the above values in equation (1).
m-v = 100(x-p) + 10(y-q) + (z-r)
=> 0 + 10*2 + 0
=>20
ANSWER:D
Answer: (D) 20
Question: How many different possible arrangements Z can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
(A) 360
(B) 720
(C) 900
(D) 1800
(E) 5040
Rationale: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's
_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!
Therefore ans Z= 7!/ (2!2!) -6!/2! = 900
HENCE C.
Answer: (C) 900
Question: How many ways can 3 friends be arranged around a circular dinner table?
(A) A)16
(B) B)2
(C) C)96
(D) D)120
(E) E)720
Rationale: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (3 - 1)! = 2! = 2.
Answer: B.
Answer: (B) B)2
Question: A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.35 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.40 In what ratio should he mix the water and milk?
(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:4
(E) 6:11
Rationale: water = w (liter)
Milk = m (liter)
==> Cost = Price x Quantity = 0.35m
==> Revenue = Price x Quantity = 0.40(m + w)
==> Profit =0.40(m+w) - 0.35m = 0.2*(0.35m)[20% of cost]
==> 0.40m + 0.40w - 0.35m = 0.07m
==> 0.02m = 0.40w
==> m/w = 0.40/0.02 = 20
--OR--
w/m = 1/20
A is correct.
Answer: (A) 1:20
Question: If x and y are positive integers, and x^3*y^4 = 16,000 which of the following is the value of xy?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 20
Rationale: 16,000 = 10^3*2^4
xy = 10*2 = 20
The answer is E.
Answer: (E) 20
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
(A) 150,287
(B) 150,219
(C) 150,200
(D) 150,298
(E) 150,217
Rationale: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:2
(3P - 100):(4P - 100) = 1:2
2P = 100 => P = 50
Their incomes = 150, 200
Answer:C
Answer: (C) 150,200
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
(A) 1:8
(B) 1:6
(C) 1:9
(D) 1:3
(E) 1:4
Rationale: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1:9
Answer: C
Answer: (C) 1:9
Question: The greatest possible length which can be used to measure exactly the length 8m ,2m 15cm, 8m 90 cm is?
(A) 25cm
(B) 101cm
(C) 56cm
(D) 42cm
(E) 5cm
Rationale: Required length = H.C.F of 800cm, 215cm, 890cm = 5cm
Answer is E
Answer: (E) 5cm
Question: The probability that B can shoot a target two out of two times is 0.45. What is the probability that the target will be missed by B immediately after such two shots?
(A) 0.25
(B) 0.5
(C) 0.55
(D) 0.4
(E) 0.8
Rationale: Suppose there are total 'x' shots.
B shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.
therefore, 2/x = 0.25 (given)
the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.
thus, the probabilty of missing just after 2 shots is (x-2)/x.
(x-2)/x = 1 - 2/x
= 1 - 0.45
= 0.55
Answer : C
Answer: (C) 0.55
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 3 days, then the fraction of the work that is left is
(A) 8/17
(B) 7/15
(C) 3/15
(D) 8/15
(E) 13/20
Rationale: Person ( A ) ( B ) ( A+B )
Time - ( 15 ) ( 20 ) (-)
Rate - ( 20 ) ( 15 ) ( 35 )
Work -(300) (300) (300)
therefore A+B requires (300/35) days to complete entire work
For 1st 4 days they work 35 * 3 = 105
Remaining work is 300 - 105 = 195
Remaining fraction of work is = 195/300 = 13/20
Answer E
Answer: (E) 13/20
Question: A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/4 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?
(A) x + 2000 = 1/3*(x - 3000)
(B) 1/3*(x - 3000) = x
(C) x + 3000 = 1/3*x
(D) x - 7000 = 1/3*x
(E) x - 3000 = 1/4*x
Rationale: Plane's original altitude = x
Plane's new altitude after ascending 2000 ft = x+2000
Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000
So, after two changes plane is at 1/4 its original altitude => x-3000 = x/4
Answer (E)
Answer: (E) x - 3000 = 1/4*x
Question: The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers
(A) 9
(B) 10
(C) 16
(D) 17
(E) 20
Rationale: The only possible sum for 4 different squares of an integer with total sum number is 95 are :
49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17)
or
81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15)
hence the answer is (D)
Answer: (D) 17
Question: If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new number is :
(A) 30
(B) 40
(C) 70
(D) 90
(E) 80
Rationale: Solution
A.M of 75 numbers = 35.
sum of 75 numbers = (75 × 35) = 2625.
total increase = (75 × 5) = 375 .
increased sum = (2625 + 375) = 3000.
increased average = 3000/75 =40 Answer B
Answer: (B) 40
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 227
(C) 268
(D) 198
(E) 176
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer:A
Answer: (A) 270
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts Q needed to confirm that each of the 5 keys matches each of the 5 locks?
(A) 5,15
(B) 4,15
(C) 5,10
(D) 4,10
(E) 5,20
Rationale: Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of Q=4 + 3 + 2 + 1 = 10 attempts.D
Answer: (D) 4,10
Question: In a class if 1 is absent the rest of them can be divided into 6 equal groups and if two are absent can be divided into 7 equal groups. Find the minimum number of students in the class
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: Multiple of 6 and 7 with difference 1 are 36 and 35
So the number of students in the class is 37
ANSWER:C
Answer: (C) 37
Question: In one hour a boat goes 18 km long the stream and 14 km against the stream.The speed of the boat in still water is?
(A) 17
(B) 18
(C) 16
(D) 15
(E) 11
Rationale: Speed in still water A = ½ ( 18+14) km/hr A= 16 kmph
Answer: C
Answer: (C) 16
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
(A) 33.5
(B) 33.4
(C) 33.3
(D) 33.1
(E) 33.7
Rationale: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer: C
Answer: (C) 33.3
Question: If a·b·c·d=270, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?
(A) 7
(B) 10
(C) 11
(D) 13
(E) 15
Rationale: prime factorize : 270 = 2*3*5*9
Hence a = 2 and d = 9 .
Hence answer is 9 - 2 = 7
Answer A
Answer: (A) 7
Question: Seven unbiased coin are tossed. What is the probability of getting almost
one head?
(A) 1/2
(B) 1/4
(C) 127/128
(D) 127/5
(E) 127/6
Rationale: Here n(S)= 2^7
Let E=event of getting atmost one head =
n(E)= 127
P(E)=n(E)/n(S)=127/128
Answer option C)
Answer: (C) 127/128
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/7
(B) 11 1/4
(C) 11 8/4
(D) 11 9/4
(E) 11 3/4
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer:B
Answer: (B) 11 1/4
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 444 km
(B) 400 km
(C) 450 km
(D) 500 km
(E) 550 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
ANSWER A
Answer: (A) 444 km
Question: If q and r are even integers, which of the following is an odd integer?
(A) qr + 2
(B) q(r − 1)
(C) q(q + 5)
(D) 3q + 4r
(E) (q + 3)(r − 1)
Rationale: If q and r are even integers, then:
A. qr + 2: even + even = even
B. q(r − 1): even(odd) = even
C. q(q + 5): even(odd) = even
D. 3q + 4r: even + even = even
E. (q + 3)(r − 1): (odd)(odd) = odd.
Answer is E.
Answer: (E) (q + 3)(r − 1)
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
(A) 2
(B) 4
(C) 5
(D) 67
(E) 9
Rationale: 1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
Answer: B
Answer: (B) 4
Question: A tap can fill a tank in 4 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 2 hr
(B) 2 hr 30 min
(C) 2 hr 50 min
(D) 2 hr 20 min
(E) 1 hr 30 min
Rationale: A tap can fill a tank in 4 hours
The tap can fill half the tank in 2 hours
Remaining part = 1/2
After half the tank is filled, three more similar taps are opened.
Hence, total number of taps becomes 4.
Part filled by one tap in 1 hour = 1/4
Part filled by four taps in 1 hour = 4×1/4=1
i.e., 4 taps can fill remaining half in 30 minutes
Total time taken = 2 hour + 30 minute = 2 hour 30 minutes
Answer is B
Answer: (B) 2 hr 30 min
Question: Jony walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:40. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 40 meters. What is Jony's speed in meters per minute?
(A) 88
(B) 100
(C) 198
(D) 216
(E) 252
Rationale: Total distance from 10 to 90 =80 + from 90 to 70 =20
So the dist is 100×40(per block dist)
Speed = 4000mts/40min =100m/min
B is the answer
Answer: (B) 100
Question: Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 19,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
(A) 1 million
(B) 1.25 million
(C) 10 million
(D) 12.6 million
(E) 125 million
Rationale: If you type that into the calculator, it results in 12.7 mil
[D], 12.6 mil, is the correct answer... see 2 posts above for quick approx method
Answer: (D) 12.6 million
Question: A train covers a certain distance at a speed of 300kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
(A) 600km/hr
(B) 700km/hr
(C) 800km/hr
(D) 900km/hr
(E) 1000km/hr
Rationale: Explanation:
Distance = 300×4 = 1200km
Required speed = (1200/2) = 600km/hr
Answer: Option A
Answer: (A) 600km/hr
Question: The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number?
(A) A)9
(B) B)10
(C) C)12
(D) D)7
(E) E)13
Rationale: The total of twelve numbers = 12X7 = 84
The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74
So, the middle number is (84 - 74 ) = 10
B
Answer: (B) B)10
Question: If 37 /2% of a number is 900,then 62 1/2% of the number is ?
(A) 1200
(B) 1350
(C) 1500
(D) 540
(E) None
Rationale: Answer
Let 371/2% of A = 900
⇒ {(75/2) x A} x 100 = 900
∴ A = (900 x 2 x 100) / 75 = 2400
So, 621/2% of A = (125/2) x (1/100) x 2400 =1500
Correct Option: C
Answer: (C) 1500
Question: P is the brother of Q and R. S is R's mother. T is P's father. Which of the following statements cannot be definitely true ?
(A) Q is K's son
(B) Q is L's son
(C) Q is S's son
(D) Q is T's son
(E) I is T's son
Rationale: Explanation:
P, Q, R are children of same parents. So. S who is R's mother and T, who is R's father will be mother and father of all three.
However, it is not mentioned whether Q is male or female So, D cannot be definitely true.
Answer: D) Q is T's son
Answer: (D) Q is T's son
Question: If Bella's income is Rs 27000, calculate her savings given that her income and expenditure are in the ratio 6:5.?
(A) Rs.4300
(B) Rs.4500
(C) Rs.7500
(D) Rs.2500
(E) Rs.5500
Rationale: Let the income and the expenditure of the person be Rs.6x and Rs.5x respectively.
Income, 6x = 27000 => x = 4500
Savings = Income - expenditure = 6x - 5x = x
So, savings = Rs.4500
Answer: B
Answer: (B) Rs.4500
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 6 shirts each of them then average number of shirt each of them now has
(A) 66
(B) 63
(C) 62
(D) 64
(E) 61
Rationale: Required average
= Old average + New average
= 60 + 6 = 66
answer :A
Answer: (A) 66
Question: How many four-digit odd numbers do not use any digit more than once?
(A) 1728
(B) 2160
(C) 2240
(D) 2268
(E) 2520
Rationale: Let a 4-digit number be represented by ABCD
Here A can have any value between 1 to 9 - so total 9
B can have any value between 0 to 9, but not A - so total 9
C can have any value between 0 to 9, but not A or B - so total 8
D can have any value between 0 to 9, but not A, B or C - so total 7
No. of ALL possible 4-digit nos (without repeating any digit) = 9*9*8*7 = 4536
Half of these would be odd.
Therefor, no. of ODD possible 4-digit nos (without repeating any digit) = 4536 / 2 = 2268
Answer should be D.
Answer: (D) 2268
Question: A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?
(A) 400
(B) 1550
(C) 1575
(D) 1600
(E) 1625
Rationale: Area Covered by Road Along the Length = 5*200 = 1000 Square Meter
Area Covered by Road Along the Width = 5*120 = 600 Square Meter
Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 5*5 = 25
Total Area of the Roads = 1000+600-25 = 1575
Answer: option C
Answer: (C) 1575
Question: Patrick has a locker with a 3 number combination. The lock contains numbers from 1 thru 30. No number may be used more than once. Patrick is superstitious and never uses numbers that end with an odd number. He also only uses 2 digit numbers. How many possible 3 digit combinations could he use?
(A) 110
(B) 440
(C) 550
(D) 880
(E) 990
Rationale: Permutation calc is: n P r = n! / (n-r)! 11 P 3 = 11!/(11-3)! = 11x10x9x(8x7x6x5x4x3x2x1)/8!=11x10x9=990 Correct answer is E (990)
Answer: (E) 990
Question: In a certain group of 9 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
(A) 40
(B) 50
(C) 74
(D) 80
(E) 100
Rationale: Case 1
1french 2either German or Spanish: 4C1 * 5C2 = 40
Case 2
2french 1either German or Spanish: 4C2 * 5C1 = 30
Case 3
3french 4C3 = 4
Answer is C = 74
Answer: (C) 74
Question: 2+9=20
3+4=19
4+3=25
5+2=34
6+1=??
Solve it?
(A) 37
(B) 26
(C) 43
(D) 42
(E) 19
Rationale: x+y=x[y+(x-1)]=x^2+xy-x
2+9=2[9+(2-1)]=4+18-2=20
3+4=3[4+(3-1)]=9+12-2=19
4+3=4[3+(4-1)]=16+12-3=25
5+2=5[2+(5-1)]=25+10-4=34
6+1=6[1+(6-1)]=36+6-5=37
Answer :A
Answer: (A) 37
Question: Of the 80 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
(A)  15
(B)  17
(C)  20
(D)  25
(E)  30
Rationale: I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
40 will be in team A
60 will be in team B
The larger diff is
70 want team A so diff is 80-40=40. At least 30 people will NOT get their wish, so for 50 researchers the same number is 20.
Answer choice C
Answer: (C)  20
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.89 km
(B) 2.88 km
(C) 3.99 km
(D) 3.78 km
(E) 3.98 km
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: (B) 2.88 km
Question: 80% of a number is added to 20, the result is the same number. Find the number?
(A) 300
(B) 288
(C) 270
(D) 100
(E) 281
Rationale: (80/100) * X + 20 = X
4x+ 100 = 5 x
x=100
Answer :: D
Answer: (D) 100
Question: Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many D women are currently in the room?
(A) 12
(B) 14
(C) 15
(D) 24
(E) 36
Rationale: the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..
let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number=5*3-3=12, then doubled=24..
ans D
Answer: (D) 24