18 questions·with explanations·for RAS, Patwari, VDO and other Rajasthan exams
Questions
Q1
In an MNC, 1000 employees are randomly selected. 500 like tea, 380 like coffee and 120 like both tea & coffee. Match the following -
1. How many people like only tea? (i) 760
2. How many people like only coffee? (ii) 640
3. How many people like neither tea nor coffee? (iii) 240
4. How many people like only one of tea or coffee? (iv) 260
5. How many people like at least one of the beverages? (v) 380
Only tea = 500 − 120 = 380, only coffee = 380 − 120 = 260, at least one = 500 + 380 − 120 = 760, neither = 1000 − 760 = 240 and only one = 380 + 260 = 640. So (1)-(v), (2)-(iv), (3)-(iii), (4)-(ii), (5)-(i).
Q2
Study the diagram given below and answer the following question -
(Figure: a rectangle for Artists, a circle for Players and a triangle for Doctors overlap. Numbers: Players only 25, Players and Doctors only 4, Doctors only 17, Players and Artists only 22, all three 3, Doctors and Artists only 8, Artists only 30)
How many doctors are both players and artists?
(1)22
(2)8
(3)3✓ Correct answer
(4)30
Answer: (3) 3
Explanation
Doctors who are also players and artists sit where the triangle, the circle and the rectangle all overlap. That region holds 3.
Q3
A clock is started at 1. By 30 minutes past 5, how many degrees has the hour hand turned through?
(1)115°
(2)135°✓ Correct answer
(3)140°
(4)155°
Answer: (2) 135°
Explanation
From 1:00 to 5:30 is 4½ hours, and the hour hand turns 30° each hour, so it turns 4.5 × 30° = 135°.
Q4
The total of the ages of P, Q and R is 90 years. What was the total of their ages five years ago?
(1)70 years
(2)75 years✓ Correct answer
(3)80 years
(4)85 years
Answer: (2) 75 years
Explanation
Five years ago each of the three was 5 years younger, so the total was 90 − 3 × 5 = 75 years.
Q5
How many 7’s are there in the given series which are immediately preceded by 6 but not immediately followed by 8?
3, 4, 8, 7, 6, 1, 5, 6, 7, 8, 4, 9, 6, 7, 5
(1)1✓ Correct answer
(2)2
(3)3
(4)4
Answer: (1) 1
Explanation
A 7 comes right after 6 twice: '6, 7, 8' and '6, 7, 5'. The first is followed by 8, so only one 7 fits.
Q6
Among three friends Amit, Bela and Chetan, exactly one speaks the truth.
Amit: 'Bela is lying.'
Bela: 'Chetan is lying.'
Chetan: 'Amit and Bela are both lying.'
Who speaks the truth?
(1)Bela✓ Correct answer
(2)Amit
(3)Chetan
(4)Cannot be determined
Answer: (1) Bela
Explanation
If Bela is truthful, Chetan lies and Amit lies, which makes exactly one truth-teller and fits every statement. If Amit were truthful, Bela would be lying, so Chetan would be truthful as well, giving two. If Chetan were truthful, Amit would be lying, making Bela truthful, which contradicts him.
Q7
Ram took half the mangoes in a basket and one more. Shyam then took half of the rest and one more, leaving 3 mangoes. How many mangoes were in the basket at first?
(1)12
(2)16
(3)18✓ Correct answer
(4)14
Answer: (3) 18
Explanation
Work backwards: before Shyam took his share there were (3 + 1) × 2 = 8 mangoes, and before Ram took his there were (8 + 1) × 2 = 18. Check: Ram takes 9 + 1 = 10, leaving 8; Shyam takes 4 + 1 = 5, leaving 3. Ignoring the 'one more' both times gives 12.
Q8
Is the whole number n an even number?
Statements: (I) n is divisible by 3.
(II) 3n + 1 is an odd number.
Which of the following is correct?
(1)Only statement (I) is sufficient
(2)Only statement (II) is sufficient✓ Correct answer
(3)Both statements (I) and (II) together are sufficient
(4)Both statements together are not sufficient
Answer: (2) Only statement (II) is sufficient
Explanation
Statement (I) alone fails, because 3 and 9 are odd while 6 and 12 are even. Statement (II) alone answers it: if 3n + 1 is odd, then 3n is even, and since 3 is odd, n must be even. So only statement (II) is sufficient.
Q9
A scholarship needs 60% or more marks and a family income under ₹2 lakh a year. How many qualify?
Marks, income (₹ lakh): Ravi 72%, 1.8; Sita 65%, 2.4; Tarun 58%, 1.2; Usha 80%, 1.5; Vimal 60%, 1.9
(1)2
(2)3✓ Correct answer
(3)4
(4)5
Answer: (2) 3
Explanation
Ravi, Usha and Vimal meet both conditions (Vimal's exactly 60% counts as '60% or more'), so 3 qualify. Sita fails on income (₹2.4 lakh) and Tarun on marks (58%); leaving out Vimal gives the wrong answer 2.
Q10
Three boxes are labelled 'Apples', 'Oranges' and 'Mixed', and every label is wrong. Without looking inside, what is the least number of fruits you must take out to label all three boxes correctly?
(1)0
(2)1✓ Correct answer
(3)2
(4)3
Answer: (2) 1
Explanation
Take one fruit from the box labelled 'Mixed': its label is wrong, so it holds only one kind, and the fruit shows which. If it is an apple, the box labelled 'Oranges' cannot hold oranges, so it holds the mixture, and the box labelled 'Apples' holds oranges (and the other way round for an orange). With no fruit taken out, two arrangements remain possible, so 0 is not enough.
Q11
All 50 students take at least one of Maths (30), Physics (25) and Chemistry (20); Maths & Physics 12, Physics & Chemistry 10, Maths & Chemistry 9, all three 6. How many take exactly two?
(1)31
(2)25
(3)19
(4)13✓ Correct answer
Answer: (4) 13
Explanation
The three 'both' counts include those who take all three, so exactly two = (12 + 10 + 9) − 3 × 6 = 31 − 18 = 13. Adding the pair counts (31) counts the all-three students three times, and subtracting 6 only once gives 25.
Q12
Which diagram best represents the relationship among Men, Women and Teachers?
(1)Three circles, each lying inside the next
(2)Two separate circles, with a third circle partly overlapping both✓ Correct answer
(3)Three separate circles, none touching another
(4)One circle inside a second, with a third overlapping both
Answer: (2) Two separate circles, with a third circle partly overlapping both
Explanation
No man is a woman, so those two circles are separate, while some men and some women are teachers (and some are not), so the teachers' circle partly overlaps both. Three separate circles would mean that no teacher is a man or a woman.
Q13
How many digits are used in all to print the page numbers of a book whose pages are numbered from 1 to 150?
(1)339
(2)450
(3)252
(4)342✓ Correct answer
Answer: (4) 342
Explanation
Pages 1–9 use 9 digits, pages 10–99 use 90 × 2 = 180 and pages 100–150 use 51 × 3 = 153, so 9 + 180 + 153 = 342. Counting only 50 three-digit pages gives 339, and giving every page three digits gives 450.
Q14
In a queue, Pooja stands exactly in the middle. Rakhi stands 6 places behind Pooja and is 9th from the back. How many persons are there in the queue?
(1)28
(2)29✓ Correct answer
(3)30
(4)31
Answer: (2) 29
Explanation
Rakhi is 9th from the back and Pooja is 6 places ahead of her, so Pooja is 15th from the back. Being exactly in the middle, she is also 15th from the front, so the queue has 15 + 15 − 1 = 29 persons. 30 counts Pooja twice.
Q15
Five teachers, Kavita, Lokesh, Meena, Naveen and Pallavi, each teach a different one of Hindi, English, Maths, Science and Sanskrit.
(i) Lokesh teaches English.
(ii) Pallavi teaches Science.
(iii) Kavita does not teach Maths.
(iv) Naveen teaches neither Maths nor Sanskrit.
Who teaches Maths?
(1)Naveen
(2)Meena✓ Correct answer
(3)Kavita
(4)Pallavi
Answer: (2) Meena
Explanation
Lokesh has English and Pallavi Science, leaving Hindi, Maths and Sanskrit for Kavita, Meena and Naveen. Naveen can take only Hindi, Kavita (not Maths) then takes Sanskrit, and Meena is left with Maths. Naveen is ruled out by clue (iv): he teaches Hindi.
Q16
Mohit, Neelam, Om, Priya, Ravi, Seema and Tarun sit around a circular table, all facing the centre.
(i) Ravi sits between Om and Priya.
(ii) Priya sits between Ravi and Seema.
(iii) Om sits immediately to the left of Tarun.
(iv) Mohit and Tarun are not neighbours.
Who sits immediately to the right of Mohit?
(1)Neelam
(2)Tarun
(3)Seema✓ Correct answer
(4)Priya
Answer: (3) Seema
Explanation
Clues (i) and (ii) put Om, Ravi, Priya, Seema in one row of neighbours, and Om is left of Tarun, so going clockwise the seats read Mohit, Neelam, Tarun, Om, Ravi, Priya, Seema (this also keeps Mohit away from Tarun). Seema, the last one before Mohit, is on his right; Neelam, on the other side, is on his left.
Q17
Arrange the following stages of life in a logical order:
1. Adult 2. Infant 3. Child 4. Old age 5. Adolescent
(1)2, 5, 3, 1, 4
(2)3, 2, 5, 1, 4
(3)2, 3, 1, 5, 4
(4)2, 3, 5, 1, 4✓ Correct answer
Answer: (4) 2, 3, 5, 1, 4
Explanation
A person is first an infant (2), then a child (3), an adolescent in the teens (5), an adult (1) and finally reaches old age (4): 2, 3, 5, 1, 4. Putting adolescence before childhood (2, 5, 3, 1, 4) reverses two stages.
Q18
A clock strikes 6 at 6 o'clock in 30 seconds, the strokes being equally spaced. How long will it take to strike 12 at 12 o'clock?
(1)60 seconds
(2)72 seconds
(3)55 seconds
(4)66 seconds✓ Correct answer
Answer: (4) 66 seconds
Explanation
Six strokes have 5 gaps, so each gap is 30 ÷ 5 = 6 seconds; twelve strokes have 11 gaps, so the time is 11 × 6 = 66 seconds. Doubling 30 to 60 wrongly treats time as proportional to the number of strokes.