JIPMAT pattern paper 1

Solution

Under y = ax + b, the mean becomes a × mean + b.

New mean = 2 × 47 − 7 = 87.

Solution

f(1) = 8.

f(8) = 36.

Solution

Expand along the first row.

= −3(5) − (5)(−8) + (0)(−7) = 25.

Solution

√(5 − |x|) needs |x| ≤ 5, that is −5 ≤ x ≤ 5.

1/√(x + 1) needs x + 1 > 0, that is x > −1.

Together: −1 < x ≤ 5, which holds for 6 integers.

Solution

Write each log with a common base: log_p q = log q / log p.

The product is (log 5 / log 3) × (log 13 / log 5) × (log 81 / log 13) = log 81 / log 3.

That is log₃ 81 = 4.

Solution

Complete the squares: (x + 6)² + (y − 6)² = 36 + 36 − 47 = 25.

Radius = √25 = 5.

Solution

Alphabetical order of the letters: A, E, L, N, P.

Words that come before it: 4 × 4! = 96 (position 1: letters before P among AELNP); 2 × 3! = 12 (position 2: letters before L among AELN); 1 × 1! = 1 (position 4: letters before N among EN).

Rank = 109 + 1 = 110.

Solution

(0, 0) to (2, 1): C(3, 2) = 3.

(2, 1) to (4, 3): C(4, 2) = 6.

Total = 18.

Solution

The angle bisector divides the opposite side in the ratio of the other two sides: BD : DC = AB : AC.

BD = 11 × 10/(10 + 4) = 7 67 cm.

Solution

A number is divisible by 9 when its digit sum is divisible by 9.

Only x = 6 works: 8496873 ÷ 9 = 944097.

Solution

|2x − 8| ≤ 2 means −2 ≤ 2x − 8 ≤ 2.

So 3 ≤ x ≤ 5.

That range contains 3 integers.

Solution

24 ≡ 3 (mod 7).

3⁶ ≡ 1 (mod 7), so powers repeat every 6.

389 = 6 × 64 + 5, so 24³⁸⁹ ≡ 3⁵ ≡ 5 (mod 7).

Solution

Hypotenuse = √(6² + 8²) = 10.

For a right triangle, r = (a + b − c)/2 = (6 + 8 − 10)/2 = 2 cm.

Solution

Adding a constant does not change the spread; multiplying by a scales the SD by |a|.

New SD = |5| × 11 = 55.

Solution

By alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper).

= (85 − 64) : (64 − 56) = 21 : 8 = 21 : 8.

Solution

Let the number be 10a + b. Reversing changes it by 9(a − b), so |a − b| = 3.

The reversed number is smaller, so the tens digit is the greater one: a − b = 3.

With a + b = 7: a = 5, b = 2. The number is 52.

Solution

Both can be at most the smaller group, 64, when every cricket fan likes the other too.

So the answer is 64.

Solution

log 3⁴⁷ = 47 × log 3 = 47 × 0.4771 = 22.4237.

A number whose log has integer part k has k + 1 digits.

The integer part is 22, so 3⁴⁷ has 23 digits.

Solution

Slope through the first two points = 0.

The third point must have the same slope from (0, 3): (k − 3)/(4 − 0) = 0.

k = 3.

Solution

If each leaves remainder r, the divisor divides every difference.

Differences: 264 and 561; their HCF is 33.

So the answer is 33 (the common remainder is 19).

Solution

Let the numbers be 8k and 3k: (8k + 3)/(3k + 3) = 52.

Solving: k = 9.

The numbers are 72 and 27; the larger is 72.

Solution

Look for x + y = 10 and xy = 21.

x = 3 and y = 7 work, since (√3 + √7)² = 3 + 7 + 2√21.

So the value is √3 + √7.

Solution

Each period of 5 years multiplies the sum by 3.

9 = 3², so it takes 2 × 5 = 10 years.

Solution

Let the number be 10a + b. Reversing changes it by 9(a − b), so |a − b| = 3.

The reversed number is larger, so the tens digit is the smaller one: a − b = −3.

With a + b = 15: a = 6, b = 9. The number is 69.

Solution

The critical points are −4, 3 and 7; x = 3 is excluded (the denominator would be 0).

For x > 7 all three factors are positive, so the expression is positive. The sign alternates across each critical point.

Negative on (3, 7) and on (−∞, −4); zero at x = −4 and x = 7. So x ≤ −4 or 3 < x ≤ 7.

Solution

n(A ∪ B ∪ C) = 47 + 47 + 31 − 18 − 11 − 15 + 8 = 89.

Exactly two = Σ(pairs) − 3(all three) = 44 − 24 = 20.

Solution

The minimum of ax² + bx + c is at x = −b/2a = 3.

Value at x = 3: (3)² − 6(3) + 15 = 6.

Solution

First term 3, common ratio −13.

Sum = 3/(1 − (−13)) = 94.

Solution

Multiply what remains after each discount: 45 × 910 × 910 = 81125.

Single discount = 35.2%.

Solution

In the third year the interest is earned on Rs. 2420: 2662 − 2420 = 242.

Rate = 2422420 × 100 = 10%.

Solution

In 2 days they finish 2 × (11105) = 22105 of the job.

B finishes the remaining 83105 in 16615 days.

Total = 2 + 16615 = 19615 days.

Solution

Σk² = n(n + 1)(2n + 1)/6 = 22 × 23 × 456 = 3795.

Solution

Expand along the first row.

= −1(−18) − (4)(9) + (−3)(15) = −63.

Solution

216, 27, 8 are perfect cubes.

213 is not.

Solution

The middle position = (51 + 1)/2 = 26.

Solution

Each letter moves 4 places forward.

S + 4 = W.

Solution

Between the two dates there are 1096 days, which leaves 4 odd days (each ordinary year gives 1, and each 29 February crossed adds 1 more).

Saturday + 4 = Wednesday.

Solution

Mohan is 28th from the left.

Between = 28 − 6 − 1 = 21.

Solution

Start from M: D is M's son. C is D's daughter.

So C is M's granddaughter.

Solution

The smaller angle is |30 × 9 − 5.5 × 20| = 160°.

Reflex angle = 360° − 160° = 200°.

Solution

The minute hand gains 5.5° per minute on the hour hand. At 6:00 the hour hand is 180° ahead.

Time = 180 ÷ 5.5 = 32 811 minutes past 6.

Solution

Each letter of MAP moves 2 places backward to give KYN.

Doing the same to GOLD: EMJB.

Solution

19 − 1 = 18 days, which leaves 4 after removing whole weeks.

Saturday + 4 = Wednesday.

Solution

Each letter moves 2 places forward.

Q + 2 = S.

Solution

With =, <, <: D = T < L < G, which gives D < G, so 'D ≤ G' holds.

With ≥, =, <: D ≥ T = L < G does not fix 'D ≤ G'.

With ≥, <, ≤: D ≥ T < L ≤ G does not fix 'D ≤ G'.

With <, =, >: D < T = L > G does not fix 'D ≤ G'.

Solution

'Some bags are boxes.' follows: no possible diagram allows 'no bags are boxes', so it must be true.

'No bags are boxes.' does not follow: it is possible that some bags are boxes.

Solution

'No fish are birds.' does not follow: it is possible that some fish are birds.

'Some cats are not birds.' does not follow: it is possible that all cats are birds.

Solution

With =, ≤, <: D = H ≤ B < C, which gives D < C, so 'D ≤ C' holds.

With ≥, =, <: D ≥ H = B < C does not fix 'D ≤ C'.

With ≤, >, <: D ≤ H > B < C does not fix 'D ≤ C'.

With =, ≤, ≥: D = H ≤ B ≥ C does not fix 'D ≤ C'.

Solution

In the morning the sun is in the East, so shadows fall towards the West.

Facing North, the West is to his left.

Solution

I alone allows (3, 1), (6, 2), (9, 3), (12, 4), (15, 5), …: the answer is always Yes.

II alone allows (5, 1), (6, 2), (7, 3), (8, 4), (9, 5), …: the answer is always Yes.

Answer: Each statement alone is sufficient.

Solution

Each letter of DOCTOR moves 2 places backward: D → B, O → M, …

So WORLD → UMPJB.

Solution

The operations alternate: × 2, + 7, × 2, + 7, …

Next: 58 × 2 = 65.

Solution

Each letter of PEN moves 3 places forward to give SHQ.

Doing the same to WIND: ZLQG.

Solution

From I alone, x can be 6, 15, 24, 33, 42: the answer is always Yes.

From II alone, x can be 42, 43, 44, 45, 46, 47, 48, 49: the answer is not fixed.

Answer: Statement I alone is sufficient, but statement II alone is not.

Solution

Each letter of GHOST moves 1 place backward: G → F, H → G, …

So PLANET → OKZMDS.

Solution

In LO, GT, BY the two letters are opposites (positions add to 27).

In HT they add to 28.

Solution

Draw the family tree: Suresh + Anita → Sanjay (married to Divya) → Sunita, Arun.

Answer: father.

Solution

Divide by 1, 2, 3, 4, … in turn.

840 ÷ 5 = 168.

Solution

Nagpur: 200 + 175 + 150 + 125 = 650.

Pune: 180 + 190 + 225 + 265 = 860.

Ratio = 650 : 860 = 65 : 86.

Solution

Pune: 180 in 2019, 265 in 2022.

Change = (265 − 180)/180 × 100 ≈ 47.2%.

Solution

Increases: Kolhapur +15; Nashik +0; Nagpur −25; Pune +35; Aurangabad −15.

The largest is Pune (+35).

Solution

Total in 2022 = 300 + 205 + 125 + 265 + 110 = 1005.

Average = 10055 = 201.

Solution

Total = 80 + 50 + 180 = 310.

Girls = 25 × 310 = 124; boys = 186.

Solution

Science students in all = 380.

College P has 80: 80380 × 100 = 21.1%.

Solution

Totals: College P 310; College Q 350; College R 480; College S 360.

The largest is College R.

Solution

Girls in each college: 25 × 310 = 124; 35 × 350 = 210; 12 × 480 = 240; 35 × 360 = 216.

Total = 790.

Solution

Simple past active → 'was/were + past participle'.

Solution

The adjective needed after 'were' meaning 'of the same family' is related.

Solution

'Information' is uncountable: no plural form, singular verb.

Solution

An order becomes 'told/ordered + object + to-infinitive'.

Solution

Adversity is hardship or misfortune; prosperity is the opposite.

Solution

'Hardly' is followed by 'when', not 'than'.

Solution

'Look forward to' is followed by the -ing form.

Solution

A 'who' question becomes 'By whom' + was + subject + past participle.

Solution

Latin: 'something for something'.

Solution

Latin: 'for this'. An ad hoc committee is formed for one task.

Solution

'Will' becomes 'would'; 'tomorrow' becomes 'the next day'.

Solution

Frugal means careful with money and resources. Poor describes having little money, not the habit of spending little.

Solution

A discovery that changes practice is pioneering (new and leading the way).

Solution

Sea-level rise threatens cities on the coast.

Solution

Stagnant water does not move; flowing water does.

Solution

'On thin ice' means: in a risky or uncertain position.

Solution

Replete means well supplied or filled, as in 'a book replete with examples'.

Solution

'By hook or by crook' means: by any means possible.

Solution

'Cattle' is a plural noun with no -s form.

Solution

'Take with a pinch of salt' means: not believe something completely.

Solution

Arrogant means having an exaggerated sense of one's importance; humble is its opposite.

Solution

French: 'already seen'.

Solution

Do not use 'more' with a comparative: 'cleverer' or 'more clever'.

Solution

Austere means strict, plain and without comfort or decoration, as in 'an austere lifestyle'.

Solution

The first paragraph says the algae supply most of the coral's food and give it colour.

Solution

Defined in the second paragraph.

Solution

The passage says bleached corals are not dead and can recover if temperatures fall soon enough.

Solution

The last sentence states this; the other efforts 'may buy time'.

Solution

Efforts that buy time postpone harm without solving the underlying problem.

Solution

The third paragraph says the answer is not to abolish rules but to leave room for judgement.

Solution

The second paragraph lists predictability, protection against favouritism and consistency.

Solution

It shows the organisation giving staff freedom to solve problems.

Solution

The first paragraph describes this build-up.

Solution

Compliance is acting according to rules or instructions.