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Sajjad1994
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Sixty stones are placed into four jars in such a way that the ratio of 30 Sep 2025, 10:42
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Sixty stones are placed into four jars in such a way that the ratio of stones in the four jars is 1:2:3:4. What is the least number of stones that can be moved, so that the ratio of stones in the four jars becomes 1:1:1:1?
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12
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Sixty stones are placed into four jars in such a way that the ratio of 30 Sep 2025, 17:03
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Sajjad1994
Sixty stones are placed into four jars in such a way that the ratio of stones in the four jars is 1:2:3:4. What is the least number of stones that can be moved, so that the ratio of stones in the four jars becomes 1:1:1:1?
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I would use a table and the unknown multiplier method, to stay organized, as shown in the screenshot at the bottom.

For a final ratio of 1:1:1:1, each jar must have 1/4 * 60 = 15 stones.

If we give 9 from the 24 to the 6, both will have 15.

If we give 3 from the 18 to the 15, both will have 15.

In total, we've moved 12 stones: 3 + 9 = 12


Another way is to just keep everything in terms of X.

We have 10x total, so each jar must have (10x / 4) = 2.5x.

If we give 1.5x from the 4x jar to the 1x jar, both will have 2.5x.

If we give .5x from the 3x jar to the 2x jar, both will have 2.5x.

In total, we've moved 2x stones: 1.5x + .5x = 2x = 12



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Sixty stones are placed into four jars in such a way that the ratio of 01 Oct 2025, 09:17
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Thank you Coach for being here in GRE forum, i am looking forward to you for more contribution in GRE world.

Cheers!

GMATCoachBen


I would use a table and the unknown multiplier method, to stay organized, as shown in the screenshot at the bottom.

For a final ratio of 1:1:1:1, each jar must have 1/4 * 60 = 15 stones.

If we give 9 from the 24 to the 6, both will have 15.

If we give 3 from the 18 to the 15, both will have 15.

In total, we've moved 12 stones: 3 + 9 = 12


Another way is to just keep everything in terms of X.

We have 10x total, so each jar must have (10x / 4) = 2.5x.

If we give 1.5x from the 4x jar to the 1x jar, both will have 2.5x.

If we give .5x from the 3x jar to the 2x jar, both will have 2.5x.

In total, we've moved 2x stones: 1.5x + .5x = 2x = 12



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Sixty stones are placed into four jars in such a way that the ratio of 04 Oct 2025, 05:36
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Official Explanation

Since the ratio is \(1:2:3:4,\) we can think of the jars containing \(1x, 2x, 3x,\) and \(4x\) marbles for some whole number, \(x.\) Then \(1x + 2x + 3x + 4x = 60,\) so \(10x = 60,\) and \(x = 6.\) This makes the current count of marbles in the jars 1(6), 2(6), 3(6), and 4(6), or 6, 12, 18, and 24. If each jar were to contain 60 ÷ 4 = 15 marbles, the ratio would become 15 : 15 : 15 : 15, which reduces to 1:1:1:1, as required. The minimum number of stones that must be moved to effect this change is 3 + 9 = 12, because three stones moved from the 18 jar to the 12 jar would leave those jars with 15 stones each, and nine stones moved from the 24 jar to the 6 jar would give those jars 15 each.

Answer: 12