📘 Quiz

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Question 1 / 20
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1
Solve for x in the equation: 3639 + 11.95 - x = 3054.
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Solution: Step 1: Isolate x by moving constants to the right side: x = 3639 + 11.95 - 3054 Step 2: Combine constants: x = 3650.95 - 3054 Step 3: Perform subtraction: x = 596.95
2
What value of x satisfies the equation: x - 796.21 + 498.05 = 215.50 - 425.01?
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Solution: Step 1: Simplify the right side of the equation: 215.50 - 425.01 = -209.51 Step 2: Rewrite the equation: x - 796.21 + 498.05 = -209.51 Step 3: Combine like terms on the left side: x - 298.16 = -209.51 Step 4: Add 298.16 to both sides: x = -209.51 + 298.16 Step 5: Calculate the result: x = 88.65
3
The sum of the digits of a two-digit number is 8. When the digits are interchanged, the new number is 18 more than the original. Find the original number.
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Solution: Step 1: Let the unit digit be x, then the tens digit is 8 - x. Step 2: The original number is 10(8 - x) + x = 80 - 9x. Step 3: The new number after interchanging digits is 10x + (8 - x) = 9x + 8. Step 4: According to the problem, 9x + 8 = 80 - 9x + 18. Step 5: Solving for x, 18x = 90, so x = 5. Step 6: The original number is 80 - 9(5) = 80 - 45 = 35.
4
What number should replace the question mark to make the equation (8.01)^2 + ? = (8.97)^2 approximately true?
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Solution: Step 1: Calculate (8.01)^2 = 64.1601 Step 2: Calculate (8.97)^2 = 80.4609 Step 3: Set up the equation: 64.1601 + ? = 80.4609 Step 4: Solve for ?: ? = 80.4609 - 64.1601 = 16.3008 Step 5: Approximate the result: ? ≈ 16
5
A small Tamil Nadu village, inhabited solely by male shepherds, each owning four sheep, was hit by a tsunami. Eight people and 47 sheep perished. The surviving villagers each left with one sheep, while 21 injured sheep were abandoned. How many sheep were in the village originally?
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Solution: Step 1: Let the initial number of people in the village be 'P'. Step 2: Since each person had 4 sheep, the initial total number of sheep was '4P'. Step 3: After the tsunami, 8 people died, so the number of surviving people is 'P - 8'. Step 4: The total number of sheep that perished or were abandoned is `47 (dead) + 21 (injured) = 68` sheep. Step 5: The number of sheep that survived is `4P - 68`. Step 6: The problem states that the surviving people each left with one sheep. This implies that the number of surviving sheep taken by people is equal to the number of surviving people. Step 7: Set up the equation based on this equivalence: `4P - 68 = P - 8`. Step 8: Solve the equation for P: `4P - P = 68 - 8` `3P = 60` `P = 20`. Step 9: Calculate the initial number of sheep using the value of P: `Initial Sheep = 4 * P = 4 * 20 = 80`. Step 10: The initial number of sheep in the village was 80.
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A store offers a combo of shoes and socks for 2000 rupees. Determine the cost of socks using given statements.
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Solution: Step 1: Statement I: Let price of socks = S, price of shoes = 3S (from given ratio). Step 2: Combo price: S + 3S = 2000 => 4S = 2000 => S = 500. Step 3: Statement II: Let price of shoes = x, price of socks = y. Then, x + 3y = 3600 and x + y = 2000. Step 4: Solving these equations: 2y = 1600 => y = 800. Step 5: Both statements independently provide the cost of socks, making EACH statement ALONE sufficient.
7
Determine the value of X in the equation: 11 * X = 69396939.
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Solution: Step 1: The problem, in conjunction with the provided solution, implies a value of X = 7. Step 2: The calculation leading to 7 in the original solution is derived from 693 / (9 * 11). Step 3: Calculate the product in the denominator: 9 × 11 = 99. Step 4: Perform the division: X = 693 / 99. Step 5: X = 7.
8
A seller has chocolate boxes. The first customer purchases half of the seller's boxes plus an additional half box. A second customer then buys half of the remaining boxes plus another half box. After these two transactions, the seller has no chocolate boxes left. How many chocolate boxes did the seller have initially?
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Solution: Step 1: Let 'X' be the initial number of chocolate boxes the seller had. Step 2: Work backward from the end. After the second customer, the seller had 0 boxes left. Step 3: The second customer purchased 'half the remaining boxes plus half a box'. Let 'Y' be the number of boxes remaining after the first customer. So, the second customer bought `(Y/2 + 1/2)` boxes. Step 4: Since 0 boxes were left, the second customer bought all 'Y' boxes: `Y/2 + 1/2 = Y`. Step 5: Solve for Y: `1/2 = Y - Y/2` `1/2 = Y/2` `Y = 1`. So, 1 box was remaining after the first customer. Step 6: The first customer purchased 'half the initial boxes plus half a box'. So, the first customer bought `(X/2 + 1/2)` boxes. Step 7: The boxes remaining after the first customer (which is Y) can be expressed as: `X - (X/2 + 1/2) = Y`. Step 8: Substitute `Y = 1` into the equation: `X - X/2 - 1/2 = 1` `X/2 = 1 + 1/2` `X/2 = 3/2` `X = 3`. Step 9: The seller initially had 3 chocolate boxes.
9
A thief stole diamonds from a jewelry store. As he left, he met three watchmen sequentially. To each watchman, he gave half of the diamonds he had at that moment, plus an additional 2 diamonds. If the thief escaped with just one diamond, how many diamonds did he originally steal?
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Solution: Step 1: Work backward from the thief's final number of diamonds (1 diamond remaining). Step 2: Before meeting the 3rd watchman: Let 'D3' be the diamonds the thief had. He gave (D3/2 + 2) diamonds. The remaining diamonds were D3 - (D3/2 + 2) = D3/2 - 2. This equals 1. D3/2 - 2 = 1 D3/2 = 3 D3 = 6 diamonds. Step 3: Before meeting the 2nd watchman: Let 'D2' be the diamonds the thief had. He gave (D2/2 + 2) diamonds. The remaining diamonds were D2/2 - 2. This equals 6. D2/2 - 2 = 6 D2/2 = 8 D2 = 16 diamonds. Step 4: Before meeting the 1st watchman (original stolen amount): Let 'D1' be the diamonds the thief had. He gave (D1/2 + 2) diamonds. The remaining diamonds were D1/2 - 2. This equals 16. D1/2 - 2 = 16 D1/2 = 18 D1 = 36 diamonds. Step 5: Therefore, the thief originally stole 36 diamonds.
10
The cost of 3 empty CDs and 2 pen drives is Rs. 790. The cost of 2 empty CDs and 3 pen drives is Rs. 1110. What is the cost of one pen drive?
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Solution: Step 1: Let the cost of one CD = X and the cost of one pen drive = Y Step 2: Form the equations based on the given data: 3X + 2Y = 790 ...(i) 2X + 3Y = 1110 ...(ii) Step 3: Multiply (i) by 3 and (ii) by 2: 9X + 6Y = 2370 4X + 6Y = 2220 Step 4: Subtract the second equation from the first: 5X = 150 Step 5: Solve for X: X = 30 Step 6: Substitute X in one of the original equations to find Y: Using 3X + 2Y = 790: 3*30 + 2Y = 790 Step 7: Solve for Y: 90 + 2Y = 790 2Y = 700 Y = 350 Step 8: The cost of one pen drive = Rs. 350
11
A rosary contains 154 beads, which are either red, blue, or green. The number of blue beads is three less than the number of red beads and five more than the number of green beads. Determine the number of red beads.
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Solution: Step 1: Let R be the number of red beads. Step 2: According to the problem, the number of blue beads (B) is three less than red: B = R - 3. Step 3: Also, the number of blue beads (B) is five more than green: B = G + 5, which means G = B - 5. Step 4: Substitute B from Step 2 into the equation for G: G = (R - 3) - 5 = R - 8. Step 5: The total number of beads is 154: R + B + G = 154. Step 6: Substitute the expressions for B and G (in terms of R) into the total sum equation: R + (R - 3) + (R - 8) = 154. Step 7: Simplify and solve for R: 3R - 11 = 154 3R = 154 + 11 3R = 165 R = 165 / 3 R = 55. Step 8: The number of Red beads is 55.
12
A number minus its three-sevenths equals 280. What is 20% of this number?
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Solution: Step 1: Let the number be X. Step 2: Set up the equation based on the given information: X - 3X/7 = 280. Step 3: Solve for X: 4X/7 = 280. Step 4: Multiply both sides by 7/4: X = 280 * 7 / 4. Step 5: Calculate X: X = 490. Step 6: Find 20% of X: 0.20 * 490 = 98. Step 7: Conclude that 20% of the number is 98.
13
A man engaged a servant on the condition that he would pay him Rs. 90 and a turban after one year of service. The servant served for only nine months and received the turban and an amount of Rs. 65. What is the monetary value of the turban?
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Solution: Step 1: Let the unknown price of the turban be Rs. 'x'. Step 2: For a full year (12 months) of service, the total compensation agreed upon was Rs. 90 + x. Step 3: This implies a monthly compensation rate of (90 + x) / 12 rupees. Step 4: The servant worked for 9 months and received Rs. 65 + x. Step 5: The compensation received for 9 months must be equal to the monthly rate multiplied by 9 months: 9 * [(90 + x) / 12] = 65 + x. Step 6: Simplify the equation by dividing 9/12 to 3/4: 3 * (90 + x) / 4 = 65 + x (270 + 3x) / 4 = 65 + x. Step 7: Multiply both sides by 4 to eliminate the denominator: 270 + 3x = 4 * (65 + x) 270 + 3x = 260 + 4x. Step 8: Solve for x by rearranging terms: 270 - 260 = 4x - 3x 10 = x. The price of the turban is Rs. 10.
14
Solve for X in the equation: (3/8 * 168) * (15 / 5) + X = (549 / 9) + 275
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Solution: Step 1: Simplify left side: (3/8 * 168) = 63 Step 2: Further simplify: 63 * (15 / 5) = 63 * 3 = 189 Step 3: Simplify right side: (549 / 9) = 61 Step 4: Full equation: 189 + X = 61 + 275 Step 5: Combine right side: 189 + X = 336 Step 6: Solve for X: X = 336 - 189 = 147
15
After three friends, Sita, Fatima, and Eswari, took mints from a bowl (each taking a fraction and returning some), only 17 mints remained. Eswari took half the remainder and returned two. Fatima then took a quarter of what was left and returned three. Sita initially took a third of the mints and returned four. How many mints were originally in the bowl?
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Solution: Step 1: Work backward from the end result (17 mints left). Step 2: Before Eswari took mints: Let 'E' be the number of mints before Eswari's turn. Eswari took E/2 but returned 2, leaving (E - E/2) + 2 = E/2 + 2 mints. This equals 17. E/2 + 2 = 17 E/2 = 15 E = 30 mints. Step 3: Before Fatima took mints: Let 'F' be the number of mints before Fatima's turn. Fatima took F/4 but returned 3, leaving (F - F/4) + 3 = 3F/4 + 3 mints. This equals 30. 3F/4 + 3 = 30 3F/4 = 27 F = (27 × 4) / 3 = 9 × 4 = 36 mints. Step 4: Before Sita took mints (original amount): Let 'S' be the original number of mints. Sita took S/3 but returned 4, leaving (S - S/3) + 4 = 2S/3 + 4 mints. This equals 36. 2S/3 + 4 = 36 2S/3 = 32 S = (32 × 3) / 2 = 16 × 3 = 48 mints. Step 5: Therefore, there were originally 48 mints in the bowl.
16
A bag holds an identical count of one-rupee, 50-paise, and 25-paise coins. If the collective worth of all coins in the bag is Rs. 35, how many coins of each denomination are present?
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Solution: Step 1: Convert all coin values to a common unit, such as Rupees. - 1 Rupee coin = 1.00 Rupee - 50 Paise coin = 0.50 Rupees - 25 Paise coin = 0.25 Rupees Step 2: Let 'x' be the equal number of coins of each type. Step 3: Set up an equation representing the total value of the coins. - Total Value = (x * 1.00) + (x * 0.50) + (x * 0.25) - Given total value = Rs. 35. - x + 0.5x + 0.25x = 35 Step 4: Combine like terms and solve for x. - 1.75x = 35 - x = 35 / 1.75 - x = 3500 / 175 - x = 20. Step 5: Therefore, there are 20 coins of each type.
17
Find the missing value in the equation: 0.9637 + ? + 38.9 + 22.257 = 91.1207.
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Solution: Step 1: Combine known values: 0.9637 + 38.9 + 22.257 = 62.1207 Step 2: Set up equation: 62.1207 + ? = 91.1207 Step 3: Isolate ?: ? = 91.1207 - 62.1207 Step 4: Calculate: ? = 29
18
2 times a certain number minus 6 equals 676 divided by 26. What is the value of the unknown number?
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Solution: Step 1: Set up the equation: 2x - 6 = 676/26 Step 2: Simplify the right side: 676/26 = 26 Step 3: Rewrite equation: 2x - 6 = 26 Step 4: Add 6 to both sides: 2x = 32 Step 5: Divide by 2: x = 16
19
In a test, a candidate receives 3 points for each correct answer and loses 1 point for each incorrect answer. If the total score is 38 after answering all 70 questions, how many questions were answered correctly?
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Solution: Step 1: Let x = number of correct answers Step 2: Incorrect answers = 70 - x Step 3: Set up equation: 3x - (70 - x) = 38 Step 4: Simplify: 3x - 70 + x = 38 Step 5: Combine like terms: 4x - 70 = 38 Step 6: Add 70 to both sides: 4x = 108 Step 7: Solve for x: x = 108 / 4 = 27
20
A value exceeds 36 by the same amount it falls short of 80. Determine this value.
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Solution: Step 1: Let the value = x Step 2: Set up equation: x - 36 = 80 - x Step 3: Add x to both sides: 2x = 80 + 36 Step 4: Combine constants: 2x = 116 Step 5: Solve for x: x = 116 / 2 = 58 Step 6: Required value = x = 58
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