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CAT 1995 Question Paper with Solutions

68 questions in 120 minutes, in three timed sections. Below: how the paper is built, the topics each section tested, and a solved sample from every section. Take the whole paper in the simulator to get your Score Waterfall, Topic ROI Map and Strategic IQ.

Paper structure and topics

VARC

Verbal Ability & Reading Comprehension

24 questions · 24 MCQ · 0 TITA

  • Reading Comprehension · 19
  • Verbal Ability · 5

DILR

Data Interpretation & Logical Reasoning

22 questions · 22 MCQ · 0 TITA

  • Data Interpretation · 15
  • Logical Reasoning · 4
  • Data Sufficiency · 3

QA

Quantitative Ability

22 questions · 22 MCQ · 0 TITA

  • Arithmetic · 8
  • Algebra · 6
  • Geometry · 4
  • Modern Math · 2
  • Number System · 2

Sample questions with solutions

14 of the 68 questions: the first passage, the first DILR set and the first QA questions of the paper.

VARC · Verbal Ability & Reading Comprehension

Passage

The Republican Party has lost its mind. To win elections, a party obviously needs votes and constituencies. However first, it needs an idea. In 1994-95, the Republican Party had after a long struggle advanced a coherent, compelling set of political ideas expressed in a specific legislative agenda. The political story of 1996 is that this same party, within the space of six weeks, became totally, shockingly intellectually deranged.

Think back. The singular achievement of the House Speaker Newt Gingrich's 1994 revolution was that it swept into power united behind one comprehensive ideological goal: dismantling the welfare state. Just about anything in the contract with America and the legislative agenda of the 104th Congress is a mere subheading: welfare reform, tax cuts, entitlement reform, returning power to the states, the balanced budget (a supremely powerful means for keeping the growth of government in check).

The central Republican idea was that the individual, the family, the church, the schools — civil society — were being systematically usurped and strangled by the federal behemoth Republicans who were riding into Washington to slay it.

With this idea they met Clinton head-on in late 1995. And although they were tactically defeated — the government shutdown proved a disaster for Republicans — they won philosophically. Clinton conceded all their principles. He finally embraced their seven year balanced budget. Then, in a State of the Union speech that might have been delivered by a moderate Republican, he declared, "The era of Big Government is over," the dominant theme of the Gingrich Revolution.

It seems so long ago. Because then, astonishingly, on the very morrow of their philosophical victory, just as the Republicans prepared to carry these ideas into battle in November, came cannon fire from the rear. The first Republican renegade to cry ‘Wrong!’ and charge was Steve Forbes. With his free-lunch, tax-cutting flat tax, he declared the balanced budget, the centrepiece of the Republican revolution, unnecessary. Then, no sooner had the Forbes mutiny been put down then Pat Buchanan declared a general insurrection. He too declared war on the party's central ideology in the name not supply side theory but of class welfare, the Democratic weapon of choice against Republicanism.

The enemy, according to Buchanan, is not the welfare state. It is that conservative icon, capitalism, with its ruthless captains of industry, greedy financiers and political elite (Republicans included, of course). All three groups collaborate to let foreigners — immigrants, traders, parasitic foreign-aid loafers — destroy the good life of the ordinary American worker.

Buchananism holds that what is killing the little guy in America is the Big Guy, not Big Government. It blames not an overreaching government that tries to insulate citizens from life's buffeting to the point where it creates deeply destructive dependency, but an uncaring government that does not protect its victim-people enough from that buffeting. Buchanan would protect and wield a mighty government apparatus to do so, government that builds trade walls and immigrant — repelling fences, that imposes punitive taxes on imports, that policies the hiring and firing practices of business with the arrogance of the most zealous affirmative action enforcer.

This is Reaganism standing on its head. Republicans have focused too much on the mere technical dangers posed by this assault. Yes, it gives ammunition to the Democrats. Yes, it puts the eventual nominee through a bruising campaign and delivers him tarnished and drained into the ring against Bill Clinton.

But the real danger is philosophical, not tactical. It is axioms, not just policies, that are under fire. The Republican idea of smaller government is being proud to dust — by Republicans. In the middle of an election year, when they should be honing their themes against Democratic liberalism, Buchanan's rise is forcing a pointless rearguard battle against a philosophical corpse, the obsolete Palaeo conservatism — a mix of nativism, protectionism and isolationism of the 1930s.

As the candidates' debate in Arizona last week showed, the entire primary campaign will be fought on Buchanan's grounds, fending off his Smoot-Hawley-Franco populism. And then what? After the convention, what does the nominee do? Try to resurrect the anti-welfare state themes of the historically successful 1994 congressional campaign? Well, yes, but with a terrible loss of energy and focus — and support. Buchanan's constituency, by then convinced by their leader that the working man's issues have been pushed aside, may simply walk on election day or, even worse, defect to the Democrats. After all, Democrats fight class war very well.

Political parties can survive bruising primary battles. They cannot survive ideological meltdown. Dole and Buchanan say they are fighting for the heart and soul of the Republican Party, heart and soul, however, will get you nowhere when you've lost your way — and your mind.

Question 1 · MCQ

Which broad ideology helped Newt Gingrich lead the Republican revolution of 1994?
  1. A.
    Tax cuts
  2. B.
    Entitlement reform
  3. C.
    Welfare reform
  4. D.
    Welfare state dismantling
    ✓ Correct
Solution
The passage says the 1994 Republican revolution was 'united behind one comprehensive ideological goal: dismantling the welfare state.' It adds that welfare reform, tax cuts, and entitlement reform are mere subheadings of that goal. Hence the broad ideology is welfare state dismantling.

Question 2 · MCQ

Assuming the passage to be truthful, what does a party not need to win elections?
  1. A.
    Votes
  2. B.
    Money
    ✓ Correct
  3. C.
    Constituencies
  4. D.
    Ideas
Solution
The opening lines list what a party needs to win elections: votes, constituencies, and first of all an idea. Money is never mentioned as a requirement in the passage, so it is the item a party does not need.

Question 3 · MCQ

Which of the following is not a Republican?
  1. A.
    Newt Gingrich
  2. B.
    Pat Buchanan
  3. C.
    Bob Dole
  4. D.
    None of these
    ✓ Correct
Solution
Newt Gingrich is identified as the Republican House Speaker, Pat Buchanan is described as leading a Republican insurrection, and Bob Dole is named alongside Buchanan as fighting for the Republican Party. Therefore all three are Republicans, so the correct answer is 'None of these.'

Question 4 · MCQ

The Republicans were tactically defeated by the Democrats because
  1. A.
    of the shutdown of the government.
    ✓ Correct
  2. B.
    the balanced budget plan failed.
  3. C.
    Steve Forbes led a revolution.
  4. D.
    Bill Clinton pre-empted them.
Solution
The passage states that the Republicans 'were tactically defeated — the government shutdown proved a disaster for Republicans.' Thus the tactical defeat was due to the shutdown of the government.

Question 5 · MCQ

Which of the following would be a suitable title for the passage?
  1. A.
    The Democrats: Victory in Sight
  2. B.
    Follies and Foibles of the Republican Party
  3. C.
    Republicans — Are You Crazy?
    ✓ Correct
  4. D.
    Mutinies on the Republican Party.
Solution
The passage opens by declaring that the Republican Party 'has lost its mind' and later describes its 'ideological meltdown,' ending with 'lost your way — and your mind.' The title 'Republicans — Are You Crazy?' directly captures this central accusation. 'Follies and foibles' is too mild, and the mutiny title covers only the Forbes/Buchanan rebellions.

DILR · Data Interpretation & Logical Reasoning

Set

Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Question 1 · MCQ

How many rupees did Suvarna start with?
  1. A.
    Rs.60
  2. B.
    Rs.34
  3. C.
    Rs.66
    ✓ Correct
  4. D.
    Rs.28
Solution
Work backwards from the final amounts. In a reverse game, each non-loser's amount is halved; the loser's reverse amount = after amount + sum of non-losers' halved amounts.
Reverse stepLoserAfter (S,T,U,V)Before (S,T,U,V)
Game 4Vibha32,32,32,3216,16,16,80
Game 3Uma16,16,16,808,8,72,40
Game 2Tara8,8,72,404,68,36,20
Game 1Suvarna4,68,36,2066,34,18,10
Suvarna started with ₹66.
Answer: 3.

Question 2 · MCQ

Who started with the lowest amount?
  1. A.
    Suvarna
  2. B.
    Tara
  3. C.
    Uma
  4. D.
    Vibha
    ✓ Correct
Solution
Using the reverse reconstruction from Q1, the starting amounts are:
PlayerStarting amount
Suvarna₹66
Tara₹34
Uma₹18
Vibha₹10
Vibha started with the lowest amount.
Answer: 4.

Question 3 · MCQ

Who started with the highest amount?
  1. A.
    Suvarna
    ✓ Correct
  2. B.
    Tara
  3. C.
    Uma
  4. D.
    Vibha
Solution
Total money is always \(4 \times 32 = 128\).

Working backwards from the final ₹32 each:
StageSuvarnaTaraUmaVibha
After game 432323232
After game 316161680
After game 2887240
After game 14683620
Start66341810
In a reverse step, non-losers halve and the loser gets the remaining amount to keep the total 128.

Starting amounts: Suvarna = 66, Tara = 34, Uma = 18, Vibha = 10.
Hence Suvarna started with the highest amount.

Question 4 · MCQ

What was the amount with Uma at the end of the second round?
  1. A.
    36
  2. B.
    72
    ✓ Correct
  3. C.
    16
  4. D.
    None of these
Solution
Total money is always \(4 \times 32 = 128\).

Reverse the game outcomes:
StageSuvarnaTaraUmaVibha
After game 432323232
After game 316161680
After game 2887240
At the end of the second round, Uma had ₹72.

So the correct option is 72.

QA · Quantitative Ability

Question 1 · MCQ

\(5^6 - 1\) is divisible by
  1. A.
    13
  2. B.
    31
    ✓ Correct
  3. C.
    5
  4. D.
    None of these
Solution
\(5^6-1=15625-1=15624\)

\(15624 = 31 \times 504\), and it is not divisible by 13 or by 5 since it ends in 4.

So the number is divisible by 31.

Question 2 · MCQ

Ram purchased a flat at Rs. 1 lakh and Prem purchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were \(10\%\) and \(5\%\). After two years they exchanged their belongings and one paid the other the difference. Then
  1. A.
    Ram paid Rs. 275 to Prem
    ✓ Correct
  2. B.
    Ram paid Rs. 475 to Prem
  3. C.
    Ram paid Rs. 375 to Prem
  4. D.
    Prem paid Rs. 475 to Ram
Solution
Flat value after 2 years:
\(100000(1.1)^2=100000 \times 1.21=121000\)

Plot value after 2 years:
\(110000(1.05)^2=110000 \times 1.1025=121275\)

Difference:
\(121275-121000=275\)

The plot is costlier, so Ram pays ₹275 to Prem.

Question 3 · MCQ

A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains \(10\%\) of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is
  1. A.
    36
  2. B.
    40
  3. C.
    15
  4. D.
    20
    ✓ Correct
Solution
Let total amount be \(x\).
Price of one orange = \(\frac{x}{50}\), price of one mango = \(\frac{x}{40}\).
After retaining \(10%\) for taxi, amount left = \(0.9x\).
Cost of 20 mangoes = \(20 \times \frac{x}{40} = \frac{x}{2}\).
Remaining balance = \(0.9x - 0.5x = 0.4x\).
Number of oranges = \(\frac{0.4x}{x/50} = 20\).

Question 4 · MCQ

The value of \(\frac{55^3 + 45^3}{55^2 - 55 \times 45 + 45^2}\) is
  1. A.
    100
    ✓ Correct
  2. B.
    105
  3. C.
    125
  4. D.
    75
Solution
Use \(a^3+b^3=(a+b)(a^2-ab+b^2)\).
Here \(a=55\), \(b=45\), so
\[ \frac{55^3+45^3}{55^2-55\times45+45^2}=55+45=100. \]

Question 5 · MCQ

Which one of the following cannot be the ratio of angles in a right-angled triangle?
  1. A.
    1 : 2 : 3
  2. B.
    1 : 1 : 2
  3. C.
    1 : 3 : 6
    ✓ Correct
  4. D.
    None of these
Solution
A right-angled triangle has one angle \(90^\circ\). For a ratio \(a:b:c\), the largest part must be half the total sum.
  • \(1:2:3\): sum \(6\), largest \(3=\frac{6}{2}\) → \(30^\circ,60^\circ,90^\circ\).
  • \(1:1:2\): sum \(4\), largest \(2=\frac{4}{2}\) → \(45^\circ,45^\circ,90^\circ\).
  • \(1:3:6\): sum \(10\), largest \(6\neq5\), giving \(18^\circ,54^\circ,108^\circ\), no right angle.
So \(1:3:6\) cannot be the ratio.

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