Goldman Sachs Clock Angle at 11:55: Answer [Solved]

Answer: 27.5 degrees. At 11:55, the angle between the hour hand and the minute hand is 27.5 degrees, not 30 degrees.

The Goldman Sachs clock angle question asks a simple-looking question: how many degrees does the angle have when the clock shows 11:55? Most candidates answer 30 degrees in a hurry. They are wrong by 2.5 degrees, and that small gap is exactly what the interviewer is checking. This walkthrough derives the correct answer from first principles, so you can repeat the method for any time.

How to Solve the Goldman Sachs Clock Angle at 11:55

Start with the two speeds that drive every clock-angle question. The minute hand makes a full 360 degree turn in 60 minutes, so it moves 6 degrees every minute. The hour hand makes a full 360 degree turn in 12 hours, which is 720 minutes, so it moves 0.5 degrees every minute. The whole puzzle is the difference between those two positions at 11:55.

First, place the minute hand. At 55 minutes past the hour, the minute hand points at the 11 on the dial. In degrees measured clockwise from 12, that is 55 times 6, which is 330 degrees.

Next, place the hour hand. This is where candidates go wrong. The hour hand is not sitting exactly on the 11. It has been moving toward the 12 all hour, and by 11:55 it is almost there. From 12, its position is 11 full hours plus 55 minutes of movement: 11 times 30 degrees, plus 55 times 0.5 degrees. That is 330 plus 27.5, which is 357.5 degrees.

Finally, subtract. The hour hand at 357.5 degrees minus the minute hand at 330 degrees leaves 27.5 degrees. That is the smaller angle between the hands, and it is the answer the interviewer wants.

Hand	Speed	Position at 11:55
Minute hand	6 degrees per minute	55 x 6 = 330 degrees
Hour hand	0.5 degrees per minute	(11 x 30) + (55 x 0.5) = 357.5 degrees
Gap	Difference	357.5 – 330 = 27.5 degrees

The Goldman Sachs Clock Angle Formula, Step by Step

Once you understand the two speeds, you can use the standard clock-angle formula and check your work in seconds. For a time H hours and M minutes, the raw difference is the absolute value of 30H minus 5.5M. The 30 comes from 360 divided by 12 hours, and the 5.5 comes from the minute hand gaining 5.5 degrees on the hour hand every minute, because 6 minus 0.5 is 5.5.

Apply it to 11:55. Thirty times 11 is 330. Five point five times 55 is 302.5. Subtract: 330 minus 302.5 is 27.5 degrees. The formula agrees with the hand-by-hand calculation, which is a good sign in an interview: two routes to the same number.

One detail matters. The formula gives the raw difference, and the question normally asks for the smaller angle between the hands. If the raw difference is above 180 degrees, subtract it from 360 to get the smaller angle. At 11:55 the raw difference is already below 180, so no adjustment is needed. The reflex angle, the larger way around the dial, is 360 minus 27.5, which is 332.5 degrees. Name it only if the interviewer asks for it, and say clearly which angle you are reporting.

Three quick checks that prove the method

Test the method on times where the answer is easy to picture. At 3:15, the minute hand is at 90 degrees and the hour hand is at 97.5 degrees, because it has moved a quarter of the way from 3 toward 4. The gap is 7.5 degrees. At 6:00, the hands point in opposite directions, so the gap is 180 degrees. At 9:15, the raw difference is 187.5 degrees, so the smaller angle is 360 minus 187.5, which is 172.5 degrees. Each check follows the same two speeds, with no special case needed.

Traps That Catch Candidates on the Goldman Sachs Clock Angle

Freezing the hour hand on the 11. This is the most common error, and it gives 30 degrees. A candidate sees the minute hand on the 11, assumes the hour hand is also on the 11, and stops. In reality the hour hand has moved 27.5 degrees past the 11 toward the 12, so it sits only 2.5 degrees short of the 12. The gap is therefore 30 minus 2.5, which is 27.5 degrees. State the hour-hand movement out loud before you give a number.

Counting dial marks instead of degrees. Five minutes on a clock face is 30 degrees, because each minute mark is 6 degrees. That shortcut works for the minute hand, but it fails for the hour hand, which moves continuously rather than jumping from number to number. If you treat the hour hand as jumping, every answer with nonzero minutes will be off.

Reporting the reflex angle by accident. At some times the raw formula result is above 180 degrees, and candidates report that number without checking whether the smaller angle was asked for. At 11:55 this trap does not bite, but an interviewer may follow up with 9:15 precisely to test it. Always finish with one sentence: this is the smaller angle, and the reflex angle is 360 minus that value.

Mixing up the 5.5 in the formula. The 5.5 is the relative speed, minute hand minus hour hand, not the speed of either hand alone. If you cannot explain where 5.5 comes from, do not use the formula as a black box. Derive it in one line: 6 degrees per minute minus 0.5 degrees per minute equals 5.5 degrees per minute.

Forgetting the second hand. Standard clock-angle questions ignore the second hand unless the interviewer says otherwise. At 11:55:00 the second hand points at 12, but it does not change the angle between the hour and minute hands. If the interviewer wanted the second hand included, the question would need a precise second count.

What the Interviewer Is Testing in the Goldman Sachs Clock Angle

Strip away the clock face and this is a test of modeling a moving system, not of memorizing a formula. Here is what the interviewer is listening for:

• Continuous motion, not snapshots. Can you see that both hands move all the time, rather than picturing a clock frozen at the hour mark? In finance, the same habit matters whenever a rate, a price, or a position keeps moving while you calculate.
• Clean mental arithmetic under pressure. The numbers are small and exact: 330, 302.5, 27.5. A candidate who sets the calculation out in order, minute hand first, then hour hand, then the difference, is much easier to follow than one who jumps straight to a number.
• Checking your own answer. Strong candidates verify with a second route, such as the 30 minus 2.5 shortcut, or the formula. Two matching answers are far more convincing than one asserted answer.
• Precision about what was asked. Smaller angle or reflex angle, degrees or dial marks, hour hand position or hour number: naming each choice shows the interviewer you read the question carefully instead of pattern-matching it.

Do not just memorize that 11:55 gives 27.5 degrees. Interviewers change the time, and a memorized answer does not transfer. The transferable skill is the method: 6 degrees per minute for the minute hand, 0.5 degrees per minute for the hour hand, subtract, and take the smaller angle if needed.

Common Follow-Up Questions

What is the reflex angle at 11:55?

The reflex angle is 332.5 degrees, which is 360 minus 27.5. Report it only if the interviewer asks for the larger angle.

Why is the answer not 30 degrees?

Thirty degrees is the gap between two adjacent hour marks, but the hour hand is not on the 11 at 11:55. It has moved 27.5 degrees from the 11 toward the 12, leaving only 2.5 degrees to the 12. The minute hand sits at 330 degrees and the hour hand at 357.5 degrees, so the gap is 27.5 degrees.

Does the same method work for any time?

Yes. Place the minute hand at 6 times the minutes, place the hour hand at 30 times the hours plus 0.5 times the minutes, subtract, and if the result is above 180 degrees, subtract it from 360 for the smaller angle. That is the whole method, and it works for every time on a 12-hour dial.

Try Another Interview Brain Teaser

Warmed up? These classics from global firms use the same kind of structured thinking:

• 100 Prisoners and 1 Light Bulb Puzzle: Answer [Solved]: one signal, one chance, and a protocol that cannot fail.
• Monty Hall Problem Answer: Switch Doors [Solved]: the probability puzzle that fools almost everyone the first time.
• Bridge and Torch Puzzle Answer: Cross in 17 Minutes [Solved]: four people, one torch, and a plan faster than it looks.
• Two Doors Riddle: One Guard Lies, One Tells the Truth [Solved]: the one question that works no matter who you ask.