mathewhe/aqua_rat huggingface dataset:
Question: If a positive odd integer N has p positive factors, how many positive factors will 3N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: I have added some extra text to make this question more GMAT-like:
Let's TEST some values of N
Try N = 3
The factors of 3 are {1, 3}. Here, p =2
So, 2N = (2)(3) = 6
The factors of 6 are {1, 2, 3, 6}. So, we have a total of4
Now check the answer choices:
A) p =2No good. We want an output of4. ELIMINATE
B) 2p = (2)(2) = 4. PERFECT! KEEP B
C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE
D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST another value of N
Try N = 7
The factors of 7 are {1, 7}. Here, p =2
So, 2N = (2)(7) = 14
The factors of 14 are {1, 2, 7, 14}. So, we have a total of4
Now check the REMAINING answer choices:
B) 2p = (2)(2) =4. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST one more (non-prime) value of N
Try N = 9
The factors of 9 are {1, 3, 9}. Here, p =3
So, 2N = (2)(9) = 18
The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6
Now check the REMAINING answer choices:
B) 2p = (2)(3) =6. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
At this point, it SEEMS LIKELY that the correct answer is C
Answer: (C) P+1
Question: Income and expenditure of a man are in the ratio 4 : 3. If the income of the person is Rs. 12000, then find his savings?
(A) 2600
(B) 2700
(C) 2800
(D) 2900
(E) 3000
Rationale: Let the income and the expenditure of the person be Rs. 4x and Rs. 3x respectively.
Income, 4x = 12000
=> x = 3000
Savings = Income - expenditure
= 4x - 3x = x
So, savings =Rs.3000.
Answer: E
Answer: (E) 3000
Question: A tour group of 25 people paid a total of $670 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22
(B) $23.94
(C) $24
(D) $25.46
(E) $30
Rationale: D.
Answer: (D) $25.46
Question: A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item
(A) Rs. 480
(B) Rs. 760
(C) Rs. 860
(D) Rs. 960
(E) None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 600
= 80/100 * 600
= 480
Option A
Answer: (A) Rs. 480
Question: If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
(A) Rs. 20
(B) Rs. 21.80
(C) Rs. 22
(D) Rs. 22.33
(E) Rs. 18.33
Rationale: S.I. on Rs. (110 - 10) for a certain time = Rs. 10.
S.I. on Rs. 100 for double the time = Rs. 20.
T.D. on Rs. 120 = Rs. (120 - 100) = Rs. 20.
T.D on Rs. 110 = Rs.(20/120)x100=Rs.18.33
answer:E
Answer: (E) Rs. 18.33
Question: Two cars, Car1 and Car2 move towards each other from W and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach W starting from Y?
(A) 15.5 sec
(B) 8.4 sec
(C) 33.6 sec
(D) 31.11 sec
(E) 16.8 sec
Rationale: W--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance WY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D
Answer: (D) 31.11 sec
Question: A can finish a work in 12 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?
(A) 1/4
(B) 1/6
(C) 1/7
(D) 1/8
(E) None of these
Rationale: Explanation:
Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question
So lets solve now,
A's 1 day work = 1/12
B's 1 day work = 1/6 [because B take half the time than A]
(A+B)'s one day work =
(1/12+1/6)=1/4
So in one day 1/4 work will be done
Answer: A
Answer: (A) 1/4
Question: Find how many positive integers less than 10,000 are there such thatthe sum of the digits of the no. is divisible by 3?
(A) 3468
(B) 2378
(C) 2875
(D) 3334
(E) 3579
Rationale: If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count of such numbers =
9999
3
=
3333
99993=3333
But zero is also divisible by 3.
This makes our total count 3334
D
Answer: (D) 3334
Question: There are 3 green shirts, 2 white shirts, 5 blue shirts, and 7 red shirts in the wardrobe. What is the least number of shirts that you have to take out to make sure that you will have a matching pair?
(A) 4
(B) 7
(C) 5
(D) 2
(E) 6
Rationale: Since there are 4 colors, if you take 4 shirts, you could still have 1 shirt per color and not have a match.
Therefore, upon taking the 5th shirt, you will definitely have a match since the 5th shirt will form at least a pair with the 1st 4
So 4+1 = 5
Answer is C
Answer: (C) 5
Question: If 4a = 16b and 8b = 13c, Find a:b:c?
(A) 52:13:8
(B) 13:7:52
(C) 7:13:52
(D) 7:13:54
(E) None of these
Rationale: Explanation:
(4a = 16b ==> a/b = 16/4)
and (8b = 13c ==> b/c = 13/8)
==> a:b = 16:4 and b:c = 13:8
a:b:c = 52:13:8
Answer: Option A
Answer: (A) 52:13:8
Question: A rectangular floor is covered by a rug except for a strip 4 meters wide along each of the four edge. If the floor is 25 meters by 20 meters, what is the area of the rug in square meters?
(A) 256
(B) 266
(C) 204
(D) 224
(E) 324
Rationale: A strip of 4 meters is covering the inner rectangular rug for all 4 sides.
Length of inner rug = 25-(2*4)
breadth of inner rug= 20-(2*4)
Area of Rug= 17 * 12 = 204 sq. mt
Ânswer: C
Answer: (C) 204
Question: Ten telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of four members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?
(A) 120
(B) 126
(C) 210
(D) 1200
(E) 1260
Rationale: My ans is 10C4 = 210
C
Answer: (C) 210
Question: Find the value of
(10)150÷(10)146
(A) 10
(B) 100
(C) 1000
(D) 10000
(E) None of these
Rationale: Explanation:
=(10)150/(10)146=10(4)=10000
Option D
Answer: (D) 10000
Question: The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?
(A) 3
(B) 1
(C) 8
(D) 9
(E) 5
Rationale: 6 * 22 = 132
7 * 19 = 133
--------------
1
Answer:B
Answer: (B) 1
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
(A) 123
(B) 127
(C) 235
(D) 305
(E) 315
Rationale: HCF of 1651 ( 1657-6) and 2032 (2037-5) is 127.
ANSWER:B
Answer: (B) 127
Question: In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, 7, 14, ?, 34, 47
(A) 31
(B) 23
(C) 36
(D) 31
(E) 33
Rationale: B
23
The given sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Answer: (B) 23
Question: What is the probability of getting exactly 1 head in a single throw of five fair coins?
(A) 1/4
(B) 3/8
(C) 3/16
(D) 5/32
(E) 7/32
Rationale: One possible case is HTTTT.
P(HTTTT) = 1/2*1/2*1/2*1/2*1/2 = 1/32
There are 5C1 = 5 possible cases.
P(1 head) = 5*1/32 = 5/32
The answer is D.
Answer: (D) 5/32
Question: If a store adds 60 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 50%, what will the new inventory of chairs be?
(A) 40
(B) 60
(C) 100
(D) 180
(E) 160
Rationale: Explanation:
Letâ€™s say t = total current inventory of chairs. The first sentence states that 60 + t = (3/2)t. First solve for the current inventory:
60 + t = (3/2)t
60 = (3/2)t âˆ’ t
60 = (1/2)t
120 = t
The manager wants to increase this by 50%.
50% of 120 is 60, so the new inventory will be 180.
Answer: (D).
Answer: (D) 180
Question: Find the value of x in the sequence of numbers 5,1,6,0,4,8,x,2 if the sum of the first 7 numbers is 30 and the average is 4.
(A) 4
(B) 9
(C) 8
(D) 6
(E) 7
Rationale: Given 5+1+6+0+4+8+x =30 (36+6)/7 =6 Answer : D
Answer: (D) 6
Question: if capacity of giving milk of a cow is y litre.from this 1litre is used to make tea.rest amount is multiply by 2 and then divided by 3.calculate the result if y=13 litre.
(A) 6
(B) 5
(C) 8
(D) 9
(E) 4
Rationale: from 13 litre 1 litre used to make tea,rest amount is 12 litre.
12*2=24
now,24/3=8 litre
answer C
Answer: (C) 8
Question: Marissa, Keith and Tony all go to Disneyland many times each summer. Together, they have all gone a total of 65 times. Marissa and Keith have gone 55 times total, while Keith and Tony have gone 40 times total. How many times has Keith gone just by himself?
(A) 30
(B) 20
(C) 25
(D) 40
(E) 10
Rationale: Marissa + Keith + Tony = 65
M + K = 55
K + T = 40
Plug these each into the original formula
55 + T = 65
T = 10
Then, M + 40 = 65
M = 25
So, 25 + K + 10 = 65
Subtract 25 and 10 from each side to get Keith's total
K = 30
Answer: A
Answer: (A) 30
Question: In game of 500 points there are three participants A, B, and C. A game take place. A gives to B 80 points and to C 101 points. Then how many points can B give to C
(A) 15 points
(B) 25 points
(C) 35 points
(D) 45 points
(E) 55 points
Rationale: In the game of 500 points,
A gives B 80 points that means B got (500-80)=420
A gives B 101 points that means B got (500-101)=399
so, B:C=420:399
so, in the game of 420, B gives "21" (420-399) points to C..
so, in the game of 500, B gives to C as
500*21/420=25 points.
ANSWER:B
Answer: (B) 25 points
Question: Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.50 a kg to produce a mixture worth Rs. 6.30 a kg
(A) 2:0
(B) 2:3
(C) 2:1
(D) 8:9
(E) 2:8
Rationale: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 80 : 90 = 8 : 9
Answer: D
Answer: (D) 8:9
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 8?
(A) 61,600
(B) 64,850
(C) 64,749
(D) 49,700
(E) 56,720
Rationale: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 8
Seeing the Options After Dividing an Finding the Reminder of 2
My Answer was A
Answer: (A) 61,600
Question: (1^3 + 2^3 + 3^3 + ... + 10^3) = x?
(A) 360
(B) 380
(C) x=420
(D) 440
(E) 450
Rationale: We know that (1^3 + 2^3 + 3^3 + ... + n^3) =	1	2n(n + 1)
6
Putting n = 10, required sum = 1	x 10 x 10 x 21 = 2100/5
420
C
Answer: (C) x=420
Question: A train 300 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 17 Kmph
(B) 54 Kmph
(C) 72 Kmph
(D) 18 Kmph
(E) 19 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 300/20
S = 15 M/Sec
Speed= 15*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 54 Kmph
Answer: B
Answer: (B) 54 Kmph
Question: With a uniform speed a car covers a distance in 8 hours. Were the speed increased by 4 km/hr the same distance could be covered in 7 1⁄2 hours. What is the distance covered?
(A) 640 km
(B) 480 km
(C) 420 km
(D) Cannot be determined
(E) None of these
Rationale: Here D⁄7.5 - D⁄8 = 4
(where D is the distance in km)
⇒ 0.5 D = 4 × 8 × 7.5
⇒ D = 2 × 4 × 8 × 7.5 = 480 km
Answer B
Answer: (B) 480 km
Question: A trader mixes 10 kg of rice at Rs. 20 per kg with 20 kg of rice of other variety at Rs.40 per kg and sells the mixture at Rs. 40 per kg. His profit percent is:
(A) No profit, no loss
(B) 5%
(C) 8%
(D) 20%
(E) None of these
Rationale: C.P. of 30 kg rice = Rs. (10 x 20 + 20 x 40) = Rs. 200 + 800 = Rs. 1000.
S.P. of 30 kg rice = Rs.30x 40 = Rs. 1200
Gain =200/1000x100% =20%.
Answer: Option D
Answer: (D) 20%
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is z, what is the difference between the probability that z is even and the probability that z is odd?
(A) 1/9
(B) 1/6
(C) 2/9
(D) 1/4
(E) 1/2
Rationale: Age of Boys:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11) & (13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Answer:A
Answer: (A) 1/9
Question: Each Machine of type A has 3 steel parts and 3 chrome parts. Each machine of type B has 6 steel parts and 5 chrome parts. If a certain group of type A and type B machines has a total of 60 steel parts and 44 chrome parts, how many machines are in the group
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Look at the below representation of the problem:
Steel Chrome total
A 3 3 60 >>no. of type A machines=60/6=10
B 6 5 44 >>no. of type B machines=44/11=4
So the answer is 14 i.e C.
Hope its clear .
Answer: (C) 14
Question: When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 2 centimeter. The actual diameter of the tissue, in centimeters, is
(A)  0.005
(B)  0.002
(C)  0.001
(D)  0.0005
(E)  0.0002
Rationale: It is very easy if x is the diameter, then the magnified length is 1000x.
ince 1000x=2 then x=2/1000=0.002.
The answer is B
Answer: (B)  0.002
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 7 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 22 km
(B) 40 km
(C) 65 km
(D) 18 km
(E) 16 km
Rationale: Distance = Relative Speed * Time
= (7 + 3) * 4 = 40 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: B
Answer: (B) 40 km
Question: A cube of edge 5 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:
(A) 1:25
(B) 1.225
(C) 1:52
(D) 1:522
(E) None
Rationale: Sol.
Required ratio = 6 * 1 * 1 / 6 * 5 * 5 = 1/25 = 1:25.
Answer A
Answer: (A) 1:25
Question: A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 48 grams of protein daily, how many grams of food X are in the mixture?
(A) 200
(B) 220
(C) 240
(D) 260
(E) 280
Rationale: Let x be the number of grams of food X in the mixture.
0.1x + 0.15(400-x) = 48
0.05x = 12
x = 240
The answer is C.
Answer: (C) 240
Question: From given equation find the value of x: 2x² + 9x − 5
(A) −5
(B) -4
(C) -6
(D) 6
(E) -4
Rationale: That quadratic is factored as follows:
2x² + 9x − 5 = (2x − 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = −5.
As for the value of x that will make
2x − 1 = 0,
we must solve that little equation. (Lesson 9.)
We have:
2x = 1
x = 1
2
The solutions are:
x = 1/2 or −5
A
Answer: (A) −5
Question: 13 buckets of water fill a tank when the capacity of each bucket is 51 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 17 litres?
(A) 39
(B) 28
(C) 23
(D) 12
(E) 24
Rationale: Capacity of the tank = (13 × 51) litre
Number of buckets required of capacity of each bucket is 17 litre = 13×51/17=13×3=39
Answer is A
Answer: (A) 39
Question: The sum of the non-prime numbers between 50 and 60, non-inclusive, is
(A) 263
(B) 293
(C) 323
(D) 353
(E) 383
Rationale: sum of consecutive integers from 51 to 59, inclusive ====> (A1 + An)/2 * # of terms = (51 + 59)/2 * 9 = 55 *9 = 495
sum of non-prime numbers b/w 50 and 60, non inclusive ===> 495 - 112 (i.e., 53 + 59, being the prime #s in the range) =383
Answer: E
Answer: (E) 383
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/8%
(B) 16 6/3%
(C) 16 2/3%
(D) 18 2/3%
(E) 16 25%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: (C) 16 2/3%
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
(A) Rs:567
(B) Rs:518
(C) Rs:519
(D) Rs:500
(E) Rs:520
Rationale: P - 340 = (P*4*8)/100
P = 500
Answer:D
Answer: (D) Rs:500
Question: I. c3 - 988 = 343,
II. d2 - 72 = 49 to solve both the equations to find the values of c and d?
(A) a > b
(B) a ≥ b
(C) a < b
(D) a ≤ b
(E) a = b or the relationship between a and b cannot be established.
Rationale: Explanation:
c3 = 1331 => c= 11
d2 = 121 => d= ± 11
c≥ d
B)
Answer: (B) a ≥ b
Question: In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?
(A) 96
(B) 125
(C) 155
(D) 175
(E) 225
Rationale: Since the question stem asks for 2 members of the same gender we get the following:
1. 2-Men and 1-Woman, hence (2C5)*(1C7) = 5*2*7=70
2. 2-Women and 1-Man, hence (2C7)*(1C5) = 7*3*5 =105
Thus, the total number of ways would be: 70+105=175
ANS:D
Answer: (D) 175
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 800 that is both a prime and a palindrome. What is the sum of the digits of p?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Given that p is smallest integer greater than 800 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
E
Answer: (E) 7
Question: The 52nd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
(A) f
(B) k
(C) l
(D) j
(E) t
Rationale: a is one time, b,2 times so on...
so 52=n(n+1)/2..
0r n(n+1)= 104... now 10*11=110...9*10<104 so n= 10.. and 10th alphabet is J. ans D
Answer: (D) j
Question: How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr
(A) 1 1/5min
(B) 2 1/5min
(C) 3 1/5min
(D) 4 1/5min
(E) 5 1/5min
Rationale: Explanation:
We know that,
Time=Distance/Speed
Speed=20 km/hr=20∗5/18m/sec=50/9m/sec
Time =(400∗9/50)=72sec=1 1/5min
Option A
Answer: (A) 1 1/5min
Question: A and B invests Rs.6000 and Rs.8000 in a business. After 6 months, A withdraws half of his capital and B withdraws one-fourth of his capital. In what ratio should they share the profits at the end of the year?
(A) 13:15
(B) 9:13
(C) 9:11
(D) 13:14
(E) 9:14
Rationale: A : B
(6000*6)+(3000*6) : (8000*6)+(6000*6)
54000 : 84000
9 : 14
Answer: E
Answer: (E) 9:14
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 18-meter platform and caught it after it had traveled 53.4 meters. How many times did the ball bounce?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Ans: 6
Division of total diatance travelled will be 18+18+9+4.5+2.25+1.125+0.5 ans B
Answer: (B) 6
Question: Can anyhow help me with an easy solution for this
3, 4, 49, 5, 3, 64, 7, 6, ?
(A) 121
(B) 169
(C) 144
(D) 256
(E) 225
Rationale: 3, 4, 49, 5, 3, 64, 7, 6, ?
3+4=7 and 7^2=49
5+3=8 and 8^2=64
7+6=13 and 13^2=169
ANSWER:B
Answer: (B) 169
Question: There are 4 people of different heights standing in order of increasing height. The difference is 2 inches between the first person and the second person, and also between the second person and the third person. The difference between the third person and the fourth person is 6 inches and the average height is 77. How tall is the fourth person?
(A) 79
(B) 81
(C) 83
(D) 85
(E) 87
Rationale: Let x be the height of the first person.
Then the heights are x, x+2, x+4, and x+10.
4x+16 = 4(77) = 308
x = 73 and the fourth person has a height of 73+10 = 83 inches
The answer is C.
Answer: (C) 83
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
(A) 1677
(B) 1683
(C) 2523
(D) 3363
(E) 3565
Rationale: L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
Answer: Option B
Answer: (B) 1683
Question: The denominator of a fraction is 8 greater than the numerator. If the numerator and the denominator are increased by 5, the resulting fraction is equal to 6â„7. What is the value of the original fraction?
(A) 25/33
(B) 31/39
(C) 37/45
(D) 43/51
(E) 53/61
Rationale: Let the numerator be x.
Then the denominator is x+8.
x+5 / x+13 = 6/7.
7x+35=6x+78.
x=43.
The original fraction is 43/51.
The answer is D.
Answer: (D) 43/51
Question: A group of men decided to do a work in 15days, but 8 of them became absent. If the rest of the group did the work in 18days, Find the original number of men?
(A) 15
(B) 48
(C) 54
(D) 33
(E) 45
Rationale: Original number of men = 8*18 / (18-15) = 48
Answer is B
Answer: (B) 48
Question: The elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 6-hour period?
(A) 88
(B) 56
(C) 42
(D) 51
(E) 64
Rationale: Complete trip = 10 floors up and 10 floors down = 20 floors = 20*1/4 = 5 minutes plus 2 minutes = 7 minutes.
6 hour = 360 minutes.
In 360 minutes operator can make 360/7=51 trips.
Answer: D.
Answer: (D) 51
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 1000. then his monthly salary is
(A) Rs. 5000
(B) Rs. 6000
(C) Rs. 4000
(D) Rs. 3000
(E) Rs. 2000
Rationale: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 1000
â‡” 20 / 100x = 1000
â‡” x = 1000 Ã— 5 = 5000.
Answer A
Answer: (A) Rs. 5000
Question: A tradesman by means of his false balance defrauds to the extent of 40%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 80%
(B) 96%
(C) 92%
(D) 84%
(E) 86%
Rationale: g% = 40 + 40 + (40*40)/100
= 96%
ANSWER:B
Answer: (B) 96%
Question: Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
(A) 35 years
(B) 37 years
(C) 16 years
(D) 17 years
(E) 18 years
Rationale: Let the present ages of X and Y be 5x and 6x years respectively.
Then, (5x + 7)/(6x + 7) = 6/7
7(5x + 7) = 6(6x + 7) => x = 7
X's present age = 5x = 35 years.
Answer: A
Answer: (A) 35 years
Question: What is the average of first 21 multiples of 4 ?
(A) A)44
(B) B)77
(C) C)79
(D) D)81
(E) E)82
Rationale: Required average = 7(1+2+....+21) / 21
(4/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 44
A
Answer: (A) A)44
Question: Find the greatest number which on dividing 4351 and 5161, leaves a reminder of 8 and 10 respectively
(A) 125
(B) 111
(C) 129
(D) 101
(E) 141
Rationale: Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (4351 - 8) and (5161 -10)
= HCF (4343, 5151) = 101
Option D
Answer: (D) 101