Quant र Reasoning (SAT/GRE/GMAT) – Quant & Reasoning MCQ
Quant र Reasoning (SAT/GRE/GMAT) – English Test
Quant & Reasoning · English Proficiency & SAT/GRE/GMAT · ४०८ प्रश्न
४०८ प्रश्न उपलब्ध। मोड छान्नुहोस्:
Quant र Reasoning (SAT/GRE/GMAT): प्रश्न र उत्तर
सही लागेको विकल्पमा थिच्नुहोस्। सही भए हरियो, गलत भए रातो देखिन्छ; ३ सेकेन्डपछि सही उत्तर र व्याख्या देखिन्छ।
सही: ० / ०
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If the roots of the quadratic equation x² - 5x + 4 = 0 are α and β, what is α + β?
सही उत्तर: ख) 6
According to Vieta's formulas, for a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a. In this case, a=1 and b=-5. Therefore, α + β = -(-5)/1 = 5. The other options are incorrect as they do not apply Vieta's formulas correctly.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A number when multiplied by 3 and then increased by 8 equals 28. What is the number?
सही उत्तर: ख) 6
Let 'x' be the number. According to the problem, 3x + 8 = 28. Subtracting 8 from both sides gives 3x = 20. Dividing by 3 gives x = 20/3, which is approximately 6.67. Since 6 is closest in value and is an available option, we test: 3(6) + 8 = 18 + 8 = 26 - not correct but the best choice in this scenario.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Find the value of 'a' if (a+2)/3 = 5
सही उत्तर: घ) 11
Multiply both sides of the equation by 3: a + 2 = 15. Subtracting 2 from both sides gives a = 13. However, this answer is not in the options. It means there’s an error. Re-checking (a+2)/3=5 => 3(a+2) = 15 => 3a + 6 = 15 => 3a = 9 => a = 3.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If a sum of money increases by 5% in the first year and decreases by 5% in the second year, what is the percentage change in the sum?
सही उत्तर: क) 1%
Let the initial sum be 'P'. After a 5% increase, the amount becomes P + 0.05P = 1.05P. After a decrease of 5%, this amount becomes 1.05P - 0.05(1.05P) = 1.05P(1 - 0.05) = 1.05P(0.95) = 0.9975P. The change is 0.9975P - P = -0.0025P, which represents a decrease of 0.25% (or -0.25%). Therefore, the percentage change is 0%.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A train travels at 60 km/h. It needs to reach a destination 300 km away in 5 hours. To ensure it arrives on time, how much faster should the train travel for the last 200km?
सही उत्तर: घ) 40 km/h
First, determine the required speed to cover the entire distance in 5 hours: 300 km / 5 h = 60 km/h. The train needs to travel the first 200km at this rate. Then, we need calculate how long it takes to travel the last 200km at a speed of 60km/h which is 200/60=3.33 hours. To arrive on time, we must find an additional speed that allows travel in 200 km within the remaining time (5-3.33 =1.67 hrs). Thus at (200/1.67) approx speed of 119km/hr would be needed. The provided options are wrong.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If a number is divided by 5, the remainder is 2. When the same number is divided by 7, the remainder is 3. What is the smallest positive integer that satisfies these conditions?
सही उत्तर: क) 17
This is a classic problem involving modular arithmetic. The least common multiple of 5 and 7 is 35. We need to find a number 'x' such that x leaves a remainder of 2 when divided by 5, and a remainder of 3 when divided by 7. We can solve this by testing numbers until we find one that satisfies both conditions. 17 divided by 5 is 3 with a remainder of 2, and 17 divided by 7 is 2 with a remainder of 3. Therefore, 17 is the answer.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If a shirt costs Rs. 500 and it is sold at a discount of 20%, what is the selling price (in Rupees)?
सही उत्तर: ख) 450
A 20% discount on Rs. 500 is calculated as (20/100) * 500 = 100. The selling price is then 500 - 100 = 400 Rupees. Option '500' represents the original cost, and '600' does not align with discount calculation.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A car travels 400 kilometers in 5 hours. It then increases its speed by 20% and continues for another 2 hours. What is the total distance covered in these 7 hours?
सही उत्तर: क) 480
The initial speed is 400 km / 5 hours = 80 km/h. The increased speed is 80 + (0.20 * 80) = 104 km/h. In the next 2 hours, the distance covered is 104 km/h * 2 hours = 208 km. Therefore, the total distance is 400 km + 208 km = 608 km. The closest answer, '560', appears to be a calculation error and does not match the correct answer of 608,
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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If roots of equation x² - 5x + 6 = 0 are α and β, what is α² + β²?
सही उत्तर: क) 25
The sum of the roots (α+β) is 5, and the product of the roots (αβ) is 6. Therefore, α² + β² = (α + β)² - 2αβ = 5² - 2(6) = 25 - 12 = 13. The option ‘25’ is close due to a calculation error, but the correct answer is 13.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A shop sells a certain item for Rs. 600 after giving a 20% discount on its original price. If the cost price of the item is Rs. 450, what is the percentage profit made by the shopkeeper?
सही उत्तर: क) 33.33%
Let the original price be 'x'. The selling price after a 20% discount is x - 0.20x = 0.80x. We are given that 0.80x = 600. Solving for x, we get x = 600/0.80 = 750. The profit is the selling price minus the cost price: 750 - 450 = 300. The percentage profit is (profit / cost price) * 100 = (300/450) * 100 = 66.67%. The other options are incorrectly calculated.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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