mathewhe/aqua_rat huggingface dataset:
Question: A cistern is filled by a tap in 6 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?
(A) 81
(B) 85
(C) 88
(D) 91
(E) 95
Rationale: filling rate - leak rate = net rate
1/6.5 - leak rate = 1/7
leak rate = 2/13 - 1/7 = 1/91
The answer is D.
Answer: (D) 91
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 4, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
(A) 1/625
(B) 2/625
(C) 4/625
(D) 50/625
(E) 25/625
Rationale: I think most of the answers are missing a point. Let me try to put it across:
Total number of possible numbers are : 5x5 = 25
Correct number =1
Case 1: When he gets it right in first attempt: P(E1) = 1/25
Case 2: He gets 1st attempt wrong and second right:
When he gets it wrong then the probability of getting wrong is 24/25.
Now there are 24 cases with him and he chooses the right one this time.
Probability of right case is 1/24
Thus, P(E2) = 24/25 x 1/24
=1/25
Probability of getting it right in at most two cases = P(E1) + P(E2)
= 1/25 + 1/25
= 2/25
= 50/625
Option (D) is therefore right as most of you mentioned but the method employed was wrong.
Answer: (D) 50/625
Question: A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 210, how much must C pay as his share of rent?
(A) 45
(B) 50
(C) 54
(D) 65
(E) none
Rationale: Sol.
A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.
âˆ´ Câ€™s rent = Rs. [210* 9/35] = Rs. 54.
Answer C
Answer: (C) 54
Question: If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 3410 , R will receive
(A) 660
(B) 700
(C) 800
(D) 900
(E) None of these
Rationale: Explanation :
Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 3410 * (6/31) = 110*6 = 660. Answer : Option A
Answer: (A) 660
Question: Three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
(A) 7 m
(B) 14 m
(C) 42 m
(D) 63 m
(E) None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 42, 49, 63 = 7 m
Correct Option: A
Answer: (A) 7 m
Question: Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?
(A) 70 km/h
(B) 60 km/h
(C) 40 km/h
(D) 20 km/h
(E) 10 km/h
Rationale: Explanation:
If the speed of the faster horse be \inline f_{s} and that of slower horse be \inline s_{s} then
\inline f_{s}+s_{s}=\frac{50}{1}=50
and \inline \frac{50}{s_{s}}-\frac{50}{f_{s}}=\frac{5}{6}
Now, you can go through options.
The speed of slower horse is 20km/h
Since, 20+30=50
and \inline \frac{50}{20}-\frac{50}{30}=\frac{5}{6}
Answer: D
Answer: (D) 20 km/h
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.625 in all. Find the share of B?
(A) 130
(B) 120
(C) 218
(D) 140
(E) 145
Rationale: A+B+C = 625
A = 3B
3B+B+B-25 = 625
5B = 650
B = 130
Answer: A
Answer: (A) 130
Question: In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 7 : 12. If the shop carries 375 dogs and bunnies total in stock, how many dogs are there?
(A) 42
(B) 66
(C) 75
(D) 112
(E) 154
Rationale: Let us assume the number of dogs, cats and bunnies to be 3x, 7x and 12x
Total dogs and bunnies = 15x.
And we are given that 15x = 375.
Hence x = 25.
Dogs = 3x = 3*25 = 75 (Option C)
Answer: (C) 75
Question: If f(a)=5b, what is the value of (f(a)-f(6b)) ?
(A) 32b
(B) 25b
(C) 6a-6b
(D) 3a+2b
(E) 52a
Rationale: f(a)=5b
f(6b) = 30b
(f(6b)-f(a)) = 30b-5b = 25b
Answer is B
Answer: (B) 25b
Question: The sum of two numbers is 16. The difference is 2. What are the two numbers?
(A) 10-6
(B) 8-8
(C) 9-7
(D) 11-5
(E) 13-3
Rationale: 9+7 = 16
9 - 7 = 2
The Answer is C
Answer: (C) 9-7
Question: Insert the missing number
4, -12, 36, -108, 324, (....)
(A) -972
(B) -972
(C) 452
(D) -452
(E) 0
Rationale: 4*-3=-12
-12*-3=36
36*-3=-108
-108*-3=324
324*-3=-972
ANSWER:A
Answer: (A) -972
Question: A certain amount earns simple interest of 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(A) 35
(B) 245
(C) 350
(D) Cannot be determined
(E) None
Rationale: Explanation: We need to know the S.I., principal and time to find the rate.
Since the principal is not given, so data is inadequate.
Answer: Option D
Answer: (D) Cannot be determined
Question: A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in?
(A) 25 days
(B) 88 days
(C) 21 days
(D) 11 days
(E) 13 days
Rationale: WC = 2:1
2x + x = 1/7
x = 1/21 => 21 days
Answer: C
Answer: (C) 21 days
Question: If below equations are true,
24 $ 6 = 64
35 $ 5 = 87
63 $ 7 = 99
Then based on similar logic what's the value of below equation
88 $ 8 = ?
(A) 1729
(B) 1129
(C) 3186
(D) 2311
(E) 1611
Rationale: E
1611
Explanation:
The number on the right side is formed as (sum of digits of the 1st number)(number1/number2)
example,
24 $ 6 = 64 (2+4 = 6) (24/6 = 4)
35 $ 5 = 87 (3+5=8) (35/5 = 7)
63 $ 7 = 99 (6+3 =9) (63/7 =9)
Simillarly,
88 $ 8 = (8+8 = 16) (88/8 = 11)
Answer: (E) 1611
Question: A 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
(A) 1/4
(B) 2/5
(C) 1/2
(D) 3/5
(E) 2/3
Rationale: you can simply use this formula to avoid confusion:
w1/w2 = (A2 - Aavg)/(Avg - A1)
Here is how you will find the values of A1 an A2.
We have an overall loss (average loss). The average loss is 5 kg when 50 kg alloy is immersed.
This is a loss of (5/50)*100 = 10%.
This is Aavg
The loss of tin is 1.375 kg for every 10 kg.
This means it loses (1.375/10)*100 = 13.75% of its weight in water.
This is A1.
The loss of silver is .375 kg for every 5 kg.
This means it loses (.375/5)* 100 = 7.5% of its weight in water.
This is A2.
Weight of Tin/Weight of Silver = (Silver's loss - Avg loss)/(Avg loss - Tin's loss)
X/Y = (7.5 - 10)/(10 - 13.75) = 2/3
E
Answer: (E) 2/3
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 11 a.m
(B) 10 a.m
(C) 77 a.m
(D) 55 a.m
(E) 65 a.m
Rationale: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: B
Answer: (B) 10 a.m
Question: In an examination 65% failed in Math and 35% failed in French. If 22% failed in both. What % of students passed in both.
(A) 22%
(B) 15%
(C) 20%
(D) 30%
(E) 10%
Rationale: Passed in Math = 100 - 65 = 35%
Passed in French = 100 - 35 = 65%
Students who passed Math or French = 100 -22 = 78%
Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 35+65-78 =22%
ANSWER:A
Answer: (A) 22%
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 1
(C) 2/3
(D) 3/4
(E) 4/5
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: (A) 1/2
Question: Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
(A) 30%
(B) 32%
(C) 34%
(D) 35%
(E) 44%
Rationale: Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = Rs.5/6x30= Rs. 25.
S.P. of 30 articles = Rs.6/5x 30= Rs. 36.
Gain % =	11/25x 100% = 44%.
Answer is E.
Answer: (E) 44%
Question: The speed of a car is 100 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 50 kmph
(B) 65 kmph
(C) 75 kmph
(D) 80 kmph
(E) 90 kmph
Rationale: Explanation:
S = (100 + 60)/2 = 80 kmph
D)
Answer: (D) 80 kmph
Question: ((-1.9)(0.6) – (2.6)(1.2))/2.0 = ?
(A) -0.71
(B) 1.0
(C) 1.07
(D) 1.71
(E) -2.13
Rationale: Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option.
-2.13
Answer E
Answer: (E) -2.13
Question: When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 8
Rationale: The given number =7y86038
Sum of the odd places =8+0+8+7=23
Sum of the even places = 3+6+y
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(9+y) = divisible by 11
14 � y = divisible by 11.
Y must be 3, to make given number divisible by 11.
B
Answer: (B) 3
Question: A seller purchased some mangoes for Rs 800 and some apples for Rs. 900. He sold the mangoes at a loss of 4 percent and apples at a profit of 10 percent. Overall he make a.?
(A) 55
(B) 58
(C) 56
(D) 60
(E) 50
Rationale: Let the SP of the mangoes and apples be Rs. m and Rs. a respectively.
m = 800(1 - 4/100) = 800 - 32
a = 900(1 + 5/100) = 900 + 90
Total SP - Total CP = m + a - (800 + 900) = - 32 + 90 = Rs. 58
As this is positive, an overall profit of Rs. 500 was made.
Answer: B
Answer: (B) 58
Question: Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10%, what should be the SP?
(A) 430
(B) 450
(C) 550
(D) 590
(E) 600
Rationale: Find Selling Price to gain 10 %.
Now, we are asked to find selling price to gain 10% profit.
Hint:
Selling Price = (100 + Gain%) × C.P.
100
Selling Price = (100 + 10) × 500
100
Selling Price = (110) × 500
100
Therefore, selling Price = Rs.550
C
Answer: (C) 550
Question: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 50 mph to reach his destination. How many miles did John drive?
(A) 235 miles.
(B) 245 miles.
(C) 240 miles.
(D) 265 miles.
(E) 275 miles.
Rationale: The total distance D traveled by John is given by
D = 45 * 2 + 3 * 50 = 240 miles.
Answer C
Answer: (C) 240 miles.
Question: Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.
(A) 40%
(B) 30%
(C) 20%
(D) 10%
(E) 5%
Rationale: Explanation:
Let the sum be x
Simple interest on x for 2 years = Rs.2000
Simple interest = PRT/100
2000 = x Ã— R Ã— 2100
â‡’ x R = 100000 --- (1)
Compound Interest on x for 2 years = 2400
P(1+R/100)T âˆ’ P = 2400
x (1+R/100)2 âˆ’ x = 2400
x (1 +2R/100+R210000)âˆ’x=2400x(2R100+R210000)=2400
2xR/100 + xR2/10000 = 2400--- (2)
Substituting the value of xR from (1) in (2) ,we get
(2Ã—100000)/100 + 100000 Ã— R10000 = 2400
2000+10R = 2400
10R=400
R=40%
Answer: Option A
Answer: (A) 40%
Question: Solve x^2 – 7x = 0
(A) (0,7)
(B) (0,3)
(C) (0,2)
(D) (0,5)
(E) (0,6)
Rationale: This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved
x^2 – 7x = 0
x(x – 7) = 0
x = 0 or x – 7 = 0
x = 0 or x = 7
The solution is x = 0, 7
Ans: A
Answer: (A) (0,7)
Question: If X is the least common multiple of 90,196, and 300, which of the following is NOT a factor of X?
(A) 600
(B) 700
(C) 900
(D) 2,100
(E) 4,900
Rationale: IF X is the least common multiple of 90,196 and 300, which of the following is NOT a factor of X?
A- 600
B- 700
C- 900
D- 2100
E- 4900
90 = 2 * 3 * 3 * 5
196 = 2 * 2 * 7 * 7
300 = 2 * 2 * 3 * 5 * 5
LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7
(TWO 2, TWO 3, TWO 5, TWO 7)
600 = 2 * 2 * 2 * 3 * 5 * 5
700 = 2 * 2 * 5 * 5 * 7
900 = 2 * 2 * 3 * 3 * 5 * 5
2100 = 2 * 2 * 3 * 5 * 5 * 7
4900 = 2 * 2 * 5 * 5 * 7 * 7=A
Answer: (A) 600
Question: A number whose fifth part increased by 2 is equal to its fourth part diminished by 2 is ?
(A) 160
(B) 80
(C) 200
(D) 220
(E) None
Rationale: Answer
Let the number be N.
Then, (N/5) + 2 = (N/4) - 2
â‡’ (N/4) - (N/5) = 4
â‡’ (5N - 4N)/20 = 4
âˆ´ N = 80
Option: B
Answer: (B) 80
Question: A football player scores 3 goals in his fifth match thus increasing his average goals score by 0.2. The total number of goals in his 5 matches would be
(A) 4
(B) 6
(C) 8
(D) 11
(E) 12
Rationale: While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...
From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should go higher or lower with your next TEST.
Here, I'll start with Answer D = 11 goals
If....
Total goals = 11 goals
5th game = 3 goals
1st 4 games = 8 goals
Avg. for 4 games = 8/4 = 2 goals/game
Avg. for all 5 games = 6/5 = 2.2 goals/game
2.2*5=11
so Answer D
Answer: (D) 11
Question: A heap of coconuts is divided into groups of 2, 3 and 7 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
(A) A)31
(B) B)43
(C) C)51
(D) D)61
(E) E)71
Rationale: LCM = 42
=> 42 + 1 = 43
ANSWER:B
Answer: (B) B)43
Question: If b is an integer greater than 6, which of the following must be divisible by 3?
(A) b (b+3) (b-5)
(B) b (b+2) (b-1)
(C) b (b+1) (b-4)
(D) b (b+4) (b-2)
(E) b (b+5) (b-6)
Rationale: anything in the form of (b-1) (b) (b+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
b (b+1) (b-4) = b (b+1) ((b-1)-3) is equivalant to (b-1) (b) (b+1)
b (b+2) (b-1) is equivalant to (b+1) missing.
b (b+3) (b-5) is equivalant to (b-1) missing and b repeating.
b (b+4) (b-2) is equivalant to odd/even consqcutive integers
b (b+5) (b-6) is equivalant to (b+1) missing and b repeating.
Answer : C
Answer: (C) b (b+1) (b-4)
Question: If 144/0.144 = 14.4/x, then the value of x is:
(A) 2.
(B) 1.
(C) -1.
(D) -2.
(E) 0
Rationale: Given Expression
=[a(Power2) - b(Power 2)]/(a + b)(a - b)
=[a(Power 2 - b(Power 2)]/[a(Power 2) - b(Power 2)]
= 1.
Answer is B.
Answer: (B) 1.
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 15. What is the last numbers?
(A) 2
(B) 4
(C) 6
(D) 5
(E) 7
Rationale: A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 15
2D = 12
D = 6
ANSWER C
Answer: (C) 6
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
(B) 2.88
(C) 2.85
(D) 2.81
(E) 2.82
Rationale: Answer & 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
Question: If f(x) = 3x − √x and g(x) = x^2, what is f(g(2))?
(A) -4
(B) 10
(C) 16
(D) 32
(E) 44
Rationale: g(x) = x²
g(2) = 2² = 4
So, f(g(2)) = f(4)
f(x) = 3x − √x
So, f(4) = 3(4) − √4
= 12- 2
= 10
= B
Answer: (B) 10
Question: How many possible ways are there to select 2 stocks at random from 8 stocks?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: 8C2 = 28
The answer is B.
Answer: (B) 28
Question: The current birth rate per thousand is 32, whereas corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by
(A) 0.0021%
(B) 0.021%
(C) 2.1%
(D) 21%
(E) None
Rationale: Sol.
Net growth on 1000 = (32 - 11) = 21.
Net growth on 100 = (21/1000 × 100)% = 2.1 %.
Answer C
Answer: (C) 2.1%
Question: In the Biotechnology class of 2000, there were C graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is C equal to?
(A) 69.
(B) 71.
(C) 73.
(D) 75.
(E) 76.
Rationale: Total = 32 +45 -13 + 9 = 73 .... My first post on the forum... I hope I am correct
C is correct choice.
Answer: (C) 73.
Question: A, B and C can do a work in 6 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
(A) 2 2/3
(B) 2 2/8
(C) 2 2/0
(D) 2 2/2
(E) 2 2/1
Rationale: Work done by all three of them in one day = 1/6 + 1/8 + 1/12 = 3/8.
The number of days required = 8/3 = 2 2/3 days.
Answer:A
Answer: (A) 2 2/3
Question: A can do a piece of work in 5 days and B can do it in 4 days how long will they both work together to complete the work?
(A) 6/11
(B) 8/9
(C) 7/9
(D) 2/9
(E) 10/11
Rationale: Explanation:
A’s one day work = 1/5
B’s one day work = 1/4
(A+B)’s one day work = 1/5 + 1/4 = 9/20 => time = 20/9 = 2 2/9 days
Answer: Option D
Answer: (D) 2/9
Question: If a 3-member subcommittee is to be formed from a certain 10-member committee, how many different such subcommittee are possible?
(A) 6
(B) 18
(C) 20
(D) 120
(E) 216
Rationale: 1st member can be selected in 10 ways
2nd can be selected in 9 ways
3rd can be selected in 8 ways
So total ways : 720
But to avoid the similar scenarios 720/3!=120
ANS:D
Answer: (D) 120
Question: How many words can be formed by using all the letters of the word “DAUGHTER” so that vowels always come together vowels are never together?
(A) 4130
(B) 2540
(C) 2130
(D) 4510
(E) 4320
Rationale: Given word contains 8 different letters
When the vowels AUE are always together we may suppose
them to form an entity ,treated as one letter
then the letter to be arranged are DAHTR(AUE)
these 6 letters can be arranged in 6p6 = 6!
= 720 ways
The vowels in the group (AUE) may be arranged in 3! = 6 ways
Required number of words = 760 * 6 =4320
Ans: E
Answer: (E) 4320
Question: On an article ,the manufacturer gains 10%, the wholesale dealer 15%, and the retailer 25%, If its retail price is 1265, what is the cost of its production?
(A) 1000
(B) 800
(C) 1100
(D) 900
(E) 700
Rationale: 110/100*115/100*125/100*C.P =1265,
11/10*23/20*5/4 C.P =1265
C.P = 800
ANSWER:B
Answer: (B) 800
Question: The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
(A) 76 minutes
(B) 66 minutes
(C) 88 minutes
(D) 48 minutes
(E) 218 minutes
Rationale: Explanation:
Total time a student spends in college = 4 hours 20 minutes = 260 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (260 – 20)/5
= 48 minutes
ANSWER: D
Answer: (D) 48 minutes
Question: Choose the missing terms out of the given alternatives.
AZ, BY, CX, DW, EV, FU, GT?
(A) HS
(B) GH
(C) ED
(D) DW
(E) KN
Rationale: A
HS
The first letter moves one step forward. The second letter moves one step backward.
Answer: (A) HS
Question: Roy is now 6 years older than Julia and half of that amount older than Kelly. If in 4 years, Roy will be twice as old as Julia, then in 4 years what would be Roy’s age multiplied by Kelly’s age?
(A) 72
(B) 84
(C) 90
(D) 96
(E) 108
Rationale: R = J+6 = K+3
R+4 = 2(J+4)
(J+6)+4 = 2J+8
J = 2
R = 8
K = 5
In 4 years (R+4)(K+4) = 12*9 = 108
The answer is E.
Answer: (E) 108
Question: Ahok will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
(A) 5
(B) 6
(C) 9
(D) 24
(E) 26
Rationale: Ahok will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Answer: (A) 5
Question: Tough and Tricky questions: Number Properties.
What is the smallest positive integer x such that 225x is the cube of a positive integer?
(A) 5
(B) 15
(C) 30
(D) 60
(E) 90
Rationale: We want to know the smallest x that will make 225x a CUBE of some number. Let's call that number y.
Let's first figure out what we're working with. The prime factorization of 225 can be visualized:
...........225
......../.......\
......25.......9
...../..\....../...\
...5....5...3.....3
So, we have 5 * 5 * 3 * 3 that can be multiplied together to get 225. Now we need to figure out what we need to make 225 * x into a cube of y (y^3=225*x).
We have two 5s and two 3s. To arrange these numbers in identical sets (3,5), we need at least one more 5 and one 3. Each of these numbers will give us the value of y (3*5=15), which, multiplied by itself three times, gives us 225 * x.
Looking at the factors we need to complete the triples, we get 5 * 3 = 15. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.
Therefore, we can go with answer choice B.
If time permits, we can do a sanity check. We calculated that y should be 3 * 5, or 15. 15 * 15 * 15 = 3375. Also, 225 * 15 = 3375.
Answer: B
Answer: (B) 15
Question: If ay > 0 and yz < 0, which of the following must be negative:
(A) ayz
(B) ay(z^2)
(C) a(y^2)z
(D) x(y^2)(z^2)
(E) (x^2)(y^2)(z^2)
Rationale: ay > 0 means that ay is positive.
yz < 0 means that yz is negative.
a(y^2)z = (ay)(yz) = positive*negative = negative. Thus option C is always negative.
Answer: (C) a(y^2)z
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 22%
(B) 25%
(C) 28%
(D) 29%
(E) 21%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: How many numbers from 10 to 46 are exactly divisible by 3?
(A) 13
(B) 12
(C) 16
(D) 17
(E) 18
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45.
12 Numbers.
10/3 = 3 and 46/3 = 15 ==> 15 - 3 = 12. Therefore 12 digits
B)
Answer: (B) 12
Question: How much time will an express train of length 200 m moving at a speed of 72 kmph take to cross another express train of length 300 m, moving at 36 kmph in the same direction?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A
Answer: (A) sec
Question: Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 17 boys and 43 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?
(A) 5
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.
Table method is shown above; here is how you will use logic:
There are 6 happy boys.
There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.
We have 6 happy boys and 6 sad boys. Total we have 17 boys. So 17 - 6 - 6 = 5 boys must be neither happy nor sad.
Answer (A)
Answer: (A) 5