mathewhe/aqua_rat huggingface dataset:
Question: Find the smallest number which when divided by 13 and 15 leaves respective remainders of 2 and 4
(A) 187
(B) 197
(C) 184
(D) 219
(E) 227
Rationale: Let 'N' is the smallest number which divided by 13 and 15 leaves respective remainders of 2 and 4.
Required number = (LCM of 13 and 15) - (common difference of divisors and remainders) = (195) - (11) = 184.
ANSWER:C
Answer: (C) 184
Question: A train running at the speed of 54 km/hr crosses a pole in 7 seconds. Find the length of the train.
(A) 150 meter
(B) 105 meter
(C) 140 meter
(D) 135 meter
(E) None of these
Rationale: Explanation:
Speed = 54*(5/18) m/sec = 15 m/sec
Length of Train(Distance) = Speed * Time
=15*7=105 meter
Option B
Answer: (B) 105 meter
Question: At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
(A) 12
(B) 11
(C) 10
(D) 9
(E) 5
Rationale: A
12
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Answer: (A) 12
Question: There were two candidates in an election. Winner candidate received 70% of votes and won the election by 280 votes. Find the number of votes casted to the winning candidate?
(A) 228
(B) 744
(C) 490
(D) 199
(E) 231
Rationale: W = 70% L = 30%
70% - 30% = 40%
40% -------- 280
70% -------- ? => 280/40*70 = 490
Answer: C
Answer: (C) 490
Question: If the area of a circle decreases by 42%, then the radius of a circle decreases by
(A) 20%
(B) 18%
(C) 24%
(D) 64%
(E) None of these
Rationale: If area of a circle decreased by x % then the radius of a circle decreases by
(100−10√100−x)%=(100−10√100−42)%
= (100−10√58)%
= 100 - 76 = 24%
Answer C
Answer: (C) 24%
Question: Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
(A) 20 1/2 hours
(B) 20 1/7 hours
(C) 22 1/2 hours
(D) 20 1/3 hours
(E) 20 3/2 hours
Rationale: 1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours
Answer: A
Answer: (A) 20 1/2 hours
Question: How many arrangements of the letters of the word ‘BENGALI’ can be made if the vowels are to occupy only odd places.
(A) 334
(B) 576
(C) 776
(D) 297
(E) 271
Rationale: Explanation:
There are 7 letters in the word Bengali of these 3 are vowels and 4 consonants.
There are 4 odd places and 3 even places. 3 vowels can occupy 4 odd places in \inline {\color{Black}4P_3{}} ways and 4 constants can be arranged in \inline {\color{Black}4P_4{}} ways.
Number of words = \inline {\color{Black}4P_3{}} x \inline {\color{Black}4P_4{}}= 24 x 24 = 576
Answer: B
Answer: (B) 576
Question: The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 10 homes?
(A) $200,000
(B) $212,000
(C) $215,000
(D) $220,000
(E) $230,000
Rationale: IMO the answer has to be D.
5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 10 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 10x=120,000.
x=12,000.
The 10 houses are sold at $12,000 profit or at $212,000. (ANSWER B)
Answer: (B) $212,000
Question: Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
(A) 23
(B) 23.5
(C) 24
(D) 24.5
(E) 25
Rationale: Let the present ages of sachin and rahul be 7x and 9x
sachin is younger than rahul in 7 years
So 9x-7x=7
2x=7
x=3.5
Sachin;s age= 7x= 7*3.5=24.5
answer :D
Answer: (D) 24.5
Question: A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score?
(A) 662
(B) 678
(C) 652
(D) 642
(E) 721
Rationale: 8 * 86 = 688 – 10 = 678
ANSWER:B
Answer: (B) 678
Question: The mean of (54,824)^2 and (54,826)^2 =
(A) (54,821)^2
(B) (54,821.5)^2
(C) (54,820.5)^2
(D) (54,825)^2 + 1
(E) (54,821)^2 – 1
Rationale: 54824^2 = (54825-1)^2 = 54825^2 + 1^2 - 2*54825*1
54826^2 = (54825+1)^2 = 54825^2 +1^2 + 2*54825*1
Taking the average of above 2 , we get (54825)^2 +1
hence the answer is D
Answer: (D) (54,825)^2 + 1
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 15
(B) 12
(C) 19.7
(D) 16
(E) 18
Rationale: Total cost of the items he purchased = Rs.25
Total tax = 30 paise = 30/100
cost of tax = x
given that tax rate = 6%
(25-30/100-x)6/100=3/100
6(25-0.3-x)=30
x=19.7
ANSWER C
Answer: (C) 19.7
Question: The charge for a single room at Hotel P is 55 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G?
(A) 50%
(B) 60%
(C) 75%
(D) 80%
(E) 100%
Rationale: P = 0.45R = 0.9G
R = 0.9G/0.45 = 2G
Thus R is 100% greater than G.
The answer is E.
Answer: (E) 100%
Question: There are 16 bees in the hive , then 10 more fly. How many bees are there in all?
(A) 7
(B) 33
(C) 12
(D) 17
(E) 26
Rationale: 16+10=26 . Answer is E.
Answer: (E) 26
Question: (723+1992)2-(723-1992)2 / (723×1992)
(A) 8
(B) 6
(C) 5
(D) 7
(E) 4
Rationale: ANSWER:D
Answer: (D) 7
Question: Walking at the rate of 3 kmph a man cover certain distance in 3hr 20 min. Running at a speed of 9 kmph the man will cover the same distance in.
(A) 45 min
(B) 50 min
(C) 40 min
(D) 48 min
(E) 54 min
Rationale: Distance = Speed * time
3*10/3 = 10km
New Speed = 9 kmph
Therefore time = D/S = 10/9 = 54min
Answer : E.
Answer: (E) 54 min
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 110 inclusive?
(A) 60
(B) 95
(C) 100
(D) 105
(E) 110
Rationale: The multiples of ten from 10 to 110 inclusive would be an evenly spaced set with 11 terms - 10, 20, 30,.......110
So average = (First term + Last Term)/2 = (10 + 110)/2 = 120/2 = 60
Hence, the correct answer is A.
Answer: (A) 60
Question: A certain fruit stand sold apples for $0.80 each and bananas for $0.70 each. If a customer purchased both apples and bananas from the stand for a total of $6.50, what total number of apples and bananas did the customer purchase?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let's start with 1 apple for $0.80.
Let's subtract $0.80 from $6.50 until we get a multiple of $0.70.
$6.50, $5.70, $4.90 = 7*$0.70
The customer purchased 7 bananas and 2 apples.
The answer is B.
Answer: (B) 9
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 9 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price
(A) 70
(B) 68
(C) 66
(D) 64
(E) 62
Rationale: Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:
Assuming x motorcycles were sold every month initially.
(568000/x + 1000)(x-9) = 594000
(568/x + 1)(x-9) = 594
Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 9 = 62 bikes this month
Answer (E)
Answer: (E) 62
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be
(A) (1.5)^4
(B) 4(1.5)
(C) (1.05)^6
(D) 1 + (0.05)^4
(E) 1 + 4(0.05)
Rationale: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be
1(1.05)^6
1.05^6
C. (1.05)^6
Answer: (C) (1.05)^6
Question: A bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind?
(A) 432
(B) 288
(C) 144
(D) 72
(E) 152
Rationale: Let the number of coins of each kind be x.
=> 5x + 2x + 1x = 1152
=> 8x = 1152 => x = 144
ANSWER:C
Answer: (C) 144
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 54/r years. If Pat's parents invested $6,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
(A)  $20000
(B)  $15000
(C)  $12000
(D)  $10000
(E)  $9000
Rationale: Since investment doubles in 54/r years, then for r=6 it'll double in 54/6=~9 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $6,000*2=$12,000 .
Answer: C.
Answer: (C)  $12000
Question: In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Let us first find the fraction of green, blue and yellow balls
1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator
= 11 / 24 , add numerators
The fraction of white balls is given by
24 / 24 - 11 / 24 = 13 / 24
So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then
(13 / 24) of x = 26 balls
or (13 / 24) × x = 26
x = 26 × (24 / 13) = 48 , total number of balls
The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by
(1 / 8) of 48 = 6 balls.
correct answer is C)6
Answer: (C) 6
Question: Set M contains numbers that satisfy the condition that, if integer x is in the set then x+3 will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.
I. 5
II. 2
III. -7
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Notice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.
Now, if -4 is in the set, then -4+3=-1mustbe in the set. Since -1 is in the set then -1+3=2mustbe in the set.so do 5. Could -7 be in the set? Certainly, but we don't know that for sure.
Answer: C.
Answer: (C) I and II only
Question: An inspector rejects 0.05% of the meters as defective. How many will he examine to reject 4?
(A) 4000
(B) 8000
(C) 5000
(D) 4500
(E) 6000
Rationale: Let the number of meters to be examined be x
Then, 0.05% of x = 4
(5/100)*((1/100)*x = 4
x = 8000
Answer is B
Answer: (B) 8000
Question: What least whole no. should be added to 532869 to make it divisible by 9?
(A) 6
(B) 7
(C) 9
(D) 10
(E) 12
Rationale: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 5+3+2+8+6+9=33, the next multiple of 9 is 36.
3 must be added to 532869 to make it divisible by 9
C
Answer: (C) 9
Question: If D is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT
(A) z - w = 3(y - x)
(B) D is divisible by 8
(C) The average of w, x, y, and z is odd
(D) D is divisible by 4
(E) w + x + 8 = y + z
Rationale: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.
D = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12
Focus on the easiest options first. You see that D is not divisible by 8. Answer (B)
Answer: (B) D is divisible by 8
Question: For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 , -8?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Given sequence: {1, -3, 2, 5, -4, -6, -8}
The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.
1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.
So there are 3 pairs of consecutive terms of the sequence for which the product is negative.
Answer: C.
Answer: (C) 3
Question: Line W has the equation 3x + y = 7. Which of the following lines is perpendicular to Line W?
(A)  y = 3x + 4
(B)  y = –3x – 6
(C)  y = (1/3)x – 1
(D)  y = (–1/3)x + 2
(E)  y = (–7/3)x – 5
Rationale: I first rewrote the equation in the standard y=mx+b form. Therefore, Line W as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line W? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.
Answer: (C)  y = (1/3)x – 1
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was.
(A) 15000
(B) 2655
(C) 16888
(D) 6677
(E) 1871
Rationale: Principal = Rs. (100 x 5400)/(12*3) = Rs. 15000.
Answer:A
Answer: (A) 15000
Question: A can do a work in 30 days, B can do it in 20 days. They together under took to do a piece of work for Rs.1000, what is the share of B?
(A) Rs.500
(B) Rs.400
(C) Rs.800
(D) Rs.600
(E) Rs.200
Rationale: Explanation:
Share of their work days = 30:20
Share of their work =20:30
Share of B’s money = 3/5*1000 =600
Answer: Option D
Answer: (D) Rs.600
Question: What least number should be added to 1056, so that the sum is completely divisible by 23
(A) 4
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: Explanation:
(1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
Answer: Option C
Answer: (C) 2
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 6% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A)  2:9
(B)  2:7
(C)  1:6
(D)  1:1
(E)  1:3
Rationale: (10/100)A+(2/100)B = (6/100)(A+B)
4A =4B
=> A/B = 1/1
Answer is D.
Answer: (D)  1:1
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 56 as quotient. What is the correct quotient ?
(A) 0
(B) 12
(C) 32
(D) 20
(E) 25
Rationale: 12*56=672
672%21=32
ANSWER:C
Answer: (C) 32
Question: How many odd numbers between 10 and 1600 are the squares of integers?
(A) 9
(B) 12
(C) 15
(D) 18
(E) 21
Rationale: The numbers are the squares of 5, 7, 9,...,39 which includes 18 numbers.
The answer is D.
Answer: (D) 18
Question: How many minutes is it before 12 noon if 16 minutes ago it was three times as many minutes after 9 am?
(A) 41 minutes
(B) 49 minutes
(C) 40 minutes
(D) 42 minutes
(E) 44 minutes
Rationale: A
41 minutes
Answer: (A) 41 minutes
Question: 1394 x 1394 = ?
(A) A)1951609
(B) B)1951601
(C) C)1951602
(D) D)1943236
(E) E)1951604
Rationale: 1394 x 1394	= (1394)2
= (1400 - 6)2
= (1400)2 + (6)2 - (2 x 1400 x 6)
= 1960000 + 36 - 16800
= 1960036 - 16800
= 1943236.
Answer:D
Answer: (D) D)1943236
Question: A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
(A) 30
(B) 31 5/7
(C) 32
(D) 33
(E) 35
Rationale: Required average
= 67 x 2 + 35 x 2 + 6 x 3
2 + 2 + 3
= 134 + 70 + 18
7
=	222
7
= 31 5	years.
7
B)
Answer: (B) 31 5/7
Question: Which of the following is true about 0<|x|-x<5?
(A) -1<x<0
(B) 0<x<1
(C) 1<x<2
(D) 2<x<3
(E) 3<x<4
Rationale: when can be |x|-x be greater than 0..
NEVER when x is positive..
ONLY A is left..
you can also substitute any value within the given range to check for answer
Example - put x as -0.5 for A. -1<x<0..
so |x|-x = |-0.5|- (-0.5) = 1 and it satisfies 0<|x|-4x<5
A
Answer: (A) -1<x<0
Question: If logx y = 10 and log2 x = 1000, what is the value of y?
(A) 210002
(B) 277889
(C) 210000
(D) 27788
(E) 788291
Rationale: Explanation:
log2 x = 1000
=> x = 21000
logx y = 10
=> y = x10
= (21000)10
= 2(1000 × 10)
= 210000
Answer: Option C
Answer: (C) 210000
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.5
(B) 1.8
(C) 1.6
(D) 1.3
(E) 1.1
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer:B
Answer: (B) 1.8
Question: Factory X's bulbs work for over 5000 hours in 37% of cases, whereas factory Y's bulbs work for over 5000 hours in 75% of cases. It is known that factory X supplies 40% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
(A) 56.4%
(B) 58%
(C) 57.4%
(D) 55%
(E) 59.8%
Rationale: For X, 40% of 37% will work.
For Y, 60% of 75% will work. *60% is the rest of the bulb supply in the market.
So, the probability that a purchased bulb will work is:
0.40(0.37) = .148
0.60(0.75) = 0.45
The combined probability then is 14.8 + 45 = 59.8%
ANS E
Answer: (E) 59.8%
Question: A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %?
(A) 40%
(B) 45%
(C) 50%
(D) 65%
(E) 70%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000
Profit% = 10 × 100 = 50%
20
Profit of 50% was made by the merchant.
C
Answer: (C) 50%
Question: What least number must be added to 1145, so that the sum is completely divisible by 23 ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 8
Rationale: 50*23 = 1150
1150 - 1145 = 5
Answer : D
Answer: (D) 5
Question: A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is
(A) 145
(B) 185
(C) 253
(D) 370
(E) None
Rationale: Solution
Let the number be x.
Then 2x = 10 or x = 5. So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digit is smaller than the units digit.
Hence, required number = 253.
Answer C
Answer: (C) 253
Question: A certain manufacturer of cake, muffin, and bread mixes has 70 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) a. 1/10
(B) b. 3/10
(C) c. 1/2
(D) d. 3/7
(E) e. 9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 70
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-20-2CMB = 70
B-CB-MB-2CMB = 30
hence the probability = 30/70 = 3/7.
D
Answer: (D) d. 3/7
Question: 10, 14, 26, 42, 70, ?
(A) 112
(B) 117
(C) 132
(D) 143
(E) 114
Rationale: E
114
Each term of the series, except the first two terms, is 2 more than the sum of the preceding two terms.
Answer: (E) 114
Question: Find the least number which when divided by 33 and 8 leaves a remainder of 2 in each case.
(A) 266
(B) 268
(C) 270
(D) 272
(E) 274
Rationale: The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(33, 8) + 2 = 266.
ANSWER:A
Answer: (A) 266
Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 30
Rationale: we have 3 places (---)to fill & we can use only digits 2, 4, 5
First place can be filled in 3 ways
2nd place can be filled in 3 ways because we can repeat the digits
3rd place can be filled in 3 ways because we can repeat the digits
Total no of codes = 3 x 3 x 3= 27
but one combination (555) will not be even so total no of even codes = 27 - 1 = 26
Answer D
Answer: (D) 26
Question: A set of numbers has the property that for any number x in the set, x+2 is also in the set. If -2 is in the set, which of the following must also be in the set
1. -4
2. 4
3. 0
(A) 1 only
(B) 2 only
(C) 1 and 2 only
(D) 1 and 3 only
(E) 1,2 and 3
Rationale: If X is in the set than X+ 2 is also in the set
If -2 in the set than
-2+2= 0 is also in the set
Since + 2 is Present, 2 + 2= 4 Is also present in the set .
Therefore Ans D
Answer: (D) 1 and 3 only
Question: If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ?
(A) 13
(B) 21
(C) 23
(D) 24
(E) 25
Rationale: The reasoning is as follows:-
B) can't be answer because Y<X
D) can't be answer because it XY x YX will give 4 digit number. Thus wrong
E) can't be answer because it XY x YX will give 4 digit number. Thus wrong
A) can't be answer because it XY x YX will give 3 digit number but the middle digit will not be equal to Y. Thus wrong
The answer is C (23)
C) is the correct answer because Y>x & will give 3 digit number & middle digit is Y
Answer: (C) 23
Question: A man sells two articles for Rs.3600 each and he gains 48% on the first and loses 48% on the next. Find his total gain or loss?
(A) 9% loss
(B) 400
(C) 4000
(D) 324
(E) 23.04%loss
Rationale: (48*48)/100 = 23.04%loss
ANSWER:E
Answer: (E) 23.04%loss
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
(A) 2
(B) 3
(C) 6
(D) 7
(E) 8
Rationale: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6
C
Answer: (C) 6
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
(A) 180
(B) 787
(C) 178
(D) 179
(E) 172
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers
= (S + T)/2 = 180.
Answer:A
Answer: (A) 180
Question: When a number is divided by 6 &then multiply by 12 the answer is 13 what is the no.?
(A) 6.5
(B) 5
(C) 5.5
(D) 5.8
(E) 6
Rationale: if $x$ is the number, x/6 * 12 = 13
=> 2x = 13
=> x = 6.5
A
Answer: (A) 6.5
Question: A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6500?
(A) Rs. 5870
(B) Rs. 5991
(C) Rs. 8870
(D) Rs. 6850
(E) None of these
Rationale: Explanation:
Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130
Therefore, required sale = Rs. [(6500 * 6) – 30,130] = Rs. (39000 – 30,130) = Rs. 8870
ANSWER C
Answer: (C) Rs. 8870
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
(A) 20/68
(B) 20/63
(C) 20/69
(D) 20/64
(E) 20/62
Rationale: Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63.Answer: B
Answer: (B) 20/63