Previous Year omet Questions for Algebra

1. XAT 2024 QADI | Algebra - Progressions omet Question

In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic progression. The total number of students from Class I to V is twice the total number of students from Class VI to X. If the total number of students from Class I to IV is 462, how many students are there in Class VI?

(a)
93
(b)
88
(c)
83
(d)
77
(e)
None of the remaining options is correct

2. XAT 2023 QADI | Algebra - Progressions omet Question

Suppose Haruka has a special key ∆ in her calculator called delta key:

Rule 1: If the display shows a one-digit number, pressing delta key ∆ replaces the displayed number with twice its value.

Rule 2: If the display shows a two-digit number, pressing delta key ∆ replaces the displayed number with the sum of the two digits.

Suppose Haruka enters the value 1 and then presses delta key ∆ repeatedly.

After pressing the ∆ key for 68 times, what will be the displayed number?

(a)
7
(b)
4
(c)
10
(d)
2
(e)
8

3. XAT 2023 QADI | Algebra - Progressions omet Question

Consider a_{n + 1} = $\frac{1}{1 + \frac{1}{a_{n}}}$ for n = 1, 2, ...., 2008, 2009 where a₁ = 1. Find the value of a₁ a₂+ a₂ a₃+ a₃ a₄+ ... + a₂₀₀₈ a₂₀₀₉

(a)
_{$\frac{2009}{1000}$}
(b)
_{$\frac{2009}{2008}$}
(c)
_{$\frac{2008}{2009}$}
(d)
_{$\frac{6000}{2009}$}
(e)
_{$\frac{2008}{6000}$}

Answer: Option C

Video Explanation

Text Explanation :

Given, a_{n + 1} = $\frac{1}{1 + \frac{1}{a_{n}}}$

⇒ a₁ = 1

⇒ a₂ = $\frac{1}{1 + \frac{1}{a_{1}}}$ = $\frac{1}{2}$

⇒ a₃ = $\frac{1}{1 + \frac{1}{a_{2}}}$ = $\frac{1}{3}$
...
⇒ a_n = $\frac{1}{n}$

Now: a₁ a₂+ a₂ a₃+ a₃ a₄+ ... + a₂₀₀₈ a₂₀₀₉ = $\frac{1}{1 \times 2}$ + $\frac{1}{2 \times 3}$ + $\frac{1}{3 \times 4}$ + ... + $\frac{1}{2008 \times 2009}$

= $(\frac{1}{1} - \frac{1}{2})$ + $(\frac{1}{2} - \frac{1}{3})$ + $(\frac{1}{3} - \frac{1}{4})$ + ... + $(\frac{1}{2008} - \frac{1}{2009})$

= $\frac{1}{1} - \frac{1}{2009}$ = $\frac{2008}{2009}$

Hence, option (c).

4. SNAP 10th Dec 2023 Quant Slot 1 (Memory Based) | Algebra - Progressions omet Question

In a decreasing arithmetic progression, the sum of all its terms, except the first term, is equal to -75. The sum of all its terms except the last term is zero and the difference of the 9^th term and the 13^th term is equal to -20. What is the first term of this series.

(a)
- 40
(b)
35
(c)
- 35
(d)
None of these

5. SNAP 10th Dec 2023 Quant Slot 2 (Memory Based) | Algebra - Progressions omet Question

If the geometric mean between a and b is $\frac{a^{n + 1} + b^{n + 1}}{a^{n} + b^{n}}$ , then the value of n is:

(a)
1
(b)
-1/2
(c)
1/2
(d)
2

6. SNAP 10th Dec 2023 Quant Slot 2 (Memory Based) | Algebra - Progressions omet Question

There is an arithmetic progression such that ratio of sum of m terms and sum of n terms is m² : n² respectively. What will be the ratio of m^th term and n^th term of the given AP?

(a)
(m - 1)/(n - 1)
(b)
(m + 1)/(n + 1)
(c)
(2m - 1)/(2n - 1)
(d)
(2m + 1)/(2n + 1)

7. XAT 2022 QADI | Algebra - Progressions omet Question

A marble is dropped from a height of 3 metres onto the ground. After the hitting theground, it bounces and reaches 80% of the height from which it was dropped. This repeats multiple times. Each time it bounces, the marble reaches 80% of the height previously reached. Eventually, the marble comes to rest on the ground.
What is the maximum distance that the marble travels from the time it was dropped until it comes to rest?

(a)
15 m
(b)
27 m
(c)
24 m
(d)
12 m
(e)
30 m

Answer: Option B

Text Explanation :

Given the ball falls from a height of 3 meters.
The ball reaches a height which 0.8 times the original height every time.
Hence this is in the form of a geometric progression. We need to count distance when the ball flies upward
and downward.
Hence considering every time the ball flies upward to a series with terms :
h1, h2,..........................
Every time the ball falls down to be
d1, d2 ,...............
h1 = (0.8)*3, h2 = (0.8)*(0.8)*3 ,.........................
d1 = 3, d2 = 3*(0.8), d3 = 3*(0.8)*(0.8)................
h1 + h2 ........ = Sum of an infinite geometric progression. = 3 * 0.8(1 + 0.8 + 0.64 + ......)
The sum of an infinite GP with r less than 1 is:

$\frac{a}{1 - r}$

= 2.4 ∙ $(\frac{1}{1 - 0.8})$ = 12 meters

The sum of d1 + d2 + + ........................
= 3 + (h1 + h2 + ..................) = 15.
The total distance = 15 + 12 = 27 meters

8. XAT 2022 QADI | Algebra - Progressions omet Question

Shireen draws a circle in her courtyard. She then measures the circle’s circumference and its diameter with her measuring tape and records them as two integers, A and B respectively. She finds that A and B are coprimes, that is, their greatest common divisor is 1. She also finds their ratio, A : B, to be: 3.141614161416… (repeating endlessly).
What is A - B?

(a)
21414
(b)
7138
(c)
21417
(d)
21413
(e)
15

Answer: Option B

Text Explanation :

We have
3.1416141614161416......
= 3 + 0.1416 + 0.00001416 + 0.000000001416.....

= 3 + $\frac{1416}{10^{4}}$ + $\frac{1416}{10^{8}}$ + $\frac{1416}{10^{12}}$ + ....

Now excluding 3 we get a series with infinite Geometric progression such that first term is $\frac{1416}{10^{4}}$ and common ratio is $\frac{1}{10^{4}}$

Therefore we get sum as $\frac{a}{1 - r}$

= $\frac{\frac{1416}{10^{4}}}{1 - \frac{1}{10^{4}}}$

we get sum as $\frac{1416}{10^{4} - 1}$

= $\frac{1416}{9999}$

Now adding 3 we get value as :

$\frac{31413}{9999}$

Now adding 3 we get value A : B as :

$\frac{10471}{3333}$

So A - B will be = 7138

Hence, option (b).

9. XAT 2022 QADI | Algebra - Progressions omet Question

If both the sequences x, a1, a2, y and x, b1, b2, z are in A.P. and it is given that y > x and z < x, then which of the following values can $\{\frac{(a 1 - a 2)}{(b 1 - b 2)}\}$ possibly take?

(a)
2
(b)
5
(c)
-3
(d)
1
(e)
0

Answer: Option C

Text Explanation :

The two given sequences in AP are:

x, a1, a2, y and x, b1, b2, z.

Additionally, it is given that : y > x and z < x.

Hence the common difference is not zero for both the series :

Since y > x the common difference is positive for the first series. (Considering the common difference to be d1)

Similarly z < x the common difference is negative for the given series. (Considering the common difference to be d2)

Now for the given value:

$\frac{(a 1 - a 2)}{(b 1 - b 2)}$

The value of a1 - a2 is negative and b1 - b2 is positive.

Hence the value of $\frac{(a 1 - a 2)}{(b 1 - b 2)}$ takes a negative value.

The only possible option is -3.

The answer is option C.

10. XAT 2020 QADI | Algebra - Progressions omet Question

A man is laying stones, from start to end, along the two sides of a 200-meter-walkway. The stones are to be laid 5 meters apart from each other. When he begins, all the stones are present at the start of the walkway. He places the first stone on each side at the walkway’s start. For all the other stones, the man lays the stones first along one of the walkway’s sides, then along the other side in an exactly similar fashion. However, he can carry only one stone at a time. To lay each stone, the man walks to the spot, lays the stone, and then walks back to pick another. After laying all the stones, the man walks back to the start, which marks the end of his work. What is the total distance that the man walks in executing this work? Assume that the width of the walkway is negligible.

(a)
16,200 meters
(b)
8,200 meters
(c)
8,050 meters
(d)
16,400 meters
(e)
4,100 meters

11. XAT 2018 QADI | Algebra - Progressions omet Question

An antique store has a collection of eight clocks. At a particular moment, the displayed times on seven of the eight clocks were as follows: 1:55 pm, 2:03 pm, 2:11 pm, 2:24 pm, 2:45 pm, 3:19 pm and 4:14 pm. If the displayed times of all eight clocks form a mathematical series, then what was the displayed time on the remaining clock?

(a)
1:53 pm
(b)
1:58 pm
(c)
2:18 pm
(d)
3:08 pm
(e)
5:08 pm

12. XAT 2017 QADI | Algebra - Progressions omet Question

The sum of the series, (-100) + (-95) + (-90) + … + 110 + 115 + 120, is

(a)
0
(b)
220
(c)
340
(d)
450
(e)
None of the above

13. IIFT 2017 QA | Algebra - Progressions omet Question

In a certain sequence the term x_n is given by formula $x_{n} = 5 x_{n - 1} - \frac{3}{4} x_{n - 2 for n ≥ 2.}$

What is the value of x₃ if x₀ = 4 and x₁ = 2?

(a)
67/2
(b)
37/2
(c)
123/4
(d)
None

14. XAT 2016 QADI | Algebra - Progressions omet Question

Consider the set of numbers {1, 3, 3², 3³,…...,3¹⁰⁰}. The ratio of the last number and the sum of the remaining numbers is closest to:

(a)
1
(b)
2
(c)
3
(d)
50
(e)
99

Answer: Option B

Text Explanation :

The last number is 3¹⁰⁰.

Sum of the remaining numbers = S = 1 + 3 + 3² + … + 3⁹⁹ …(1)

This is a GP with a = 1; r = 3 and n = 100

∴ S = $\frac{1 \times (3^{100} - 1)}{3 - 1}$

∴ Required ratio = $\frac{3^{100}}{\frac{1 \times (3^{100} - 1)}{2}}$ = $\frac{2}{1 - \frac{1}{3^{100}}}$

∵ 1/3¹⁰⁰ is approximately zero, hence it can be ignored.

∴ Ratio = 2

Hence, option (b).

15. IIFT 2016 QA | Algebra - Progressions omet Question

A child, playing at the balcony of his multi-storied apartment, drops a ball from a height of 350 m. Each time the ball rebounds, it rises 4/5th of the height it has fallen through. The total distance travelled by the ball before it comes to rest is

(a)
2530 m
(b)
2800 m
(c)
3150 m
(d)
3500 m

16. IIFT 2016 QA | Algebra - Progressions omet Question

What is the sum of integers 54 through 196 inclusive?

(a)
28,820
(b)
24,535
(c)
20,250
(d)
17,875

17. IIFT 2016 QA | Algebra - Progressions omet Question

A multi-storied office building has a total of 17 rows of parking spaces. There are 20 parking spaces in the first row and 21 parking spaces in the second row. In each subsequent row, there are 2 more parking spaces than in the previous row. The total number of parking spaces in the office building is

(a)
380
(b)
464
(c)
596
(d)
712

18. IIFT 2016 QA | Algebra - Progressions omet Question

The sum of 4 + 44 + 444 + …. upto n terms in

(a)
$\frac{40}{81} (8^{n} - 1) - \frac{5 n}{9}$
(b)
$\frac{40}{81} (8^{n} - 1) - \frac{4 n}{9}$
(c)
$\frac{40}{81} (10^{n} - 1) - \frac{4 n}{9}$
(d)
$\frac{40}{81} (10^{n} - 1) - \frac{5 n}{9}$

19. IIFT 2015 QA | Algebra - Progressions omet Question

If p, q and r are three unequal numbers such that p, q and r are in A.P., and p, r-q and q-p are in G.P., then p : q : r is equal to:

(a)
1 : 2 : 3
(b)
2 : 3 : 4
(c)
3 : 2 : 1
(d)
1 : 3 : 4

20. IIFT 2015 QA | Algebra - Progressions omet Question

Seema has joined a new Company after the completion of her B.Tech from a reputed engineering college in Chennai. She saves 10% of her income in each of the first three months of her service and for every subsequent month, her savings are Rs. 50 more than the savings of the immediate previous month. If her joining income was Rs. 3000, her total savings from the start of the service will be Rs.11400 in:

(a)
6 months
(b)
12 months
(c)
18 months
(d)
24 months

21. XAT 2015 QA | Algebra - Progressions omet Question

What is the sum of the following series?
–64, –66, –68,……..….., –100

(a)
-1458
(b)
-1558
(c)
-1568
(d)
-1664
(e)
None of the above

22. XAT 2015 QA | Algebra - Progressions omet Question

An ascending series of numbers satisfies the following conditions:

When divided by 3, 4, 5 or 6, the numbers leave a remainder of 2.
When divided by 11, the numbers leave no remainder.

The 6th number in this series will be:

(a)
242
(b)
2882
(c)
3542
(d)
4202
(e)
None of the above

Algebra - Progressions - Previous Year CAT/MBA Questions

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